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The sequence a (n) is defined by : a(n) = (n-1)(n-2)(n-3). Show that the first three terms of the sequence are zero,but the rest of the terms are positive.

Posted by Komalpreet Kaur 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 2 months ago

Nth term of the sequence is given by t_n = (n - 1)(n -2 )(n -3 ), here n is integers e.g., n = 1, 2, 3, 4, .........
First term , put n = 1
Then, t₁ = (1 - 1)(1 - 2)(1 - 3) = 0 × (-1) × (-2) = 0
2nd term, put n = 2
Then, t₂ = (2 - 1)(2 - 2)(2 - 3) = 1 × 0 × (-1) = 0
3rd term , put n = 3
Then, t₃ = (3 - 1)( 3 - 2)(3 - 3) = 2 × 1 × 0 = 0
Here it is clear that first three terms of the sequence are zero.
Now, put n = 4
Then, t₄ = (4 - 1)(4 - 2)(4 - 3) = 3 × 2 × 1 = 6 > 0 e.g., positive
Put n = 5
Then, t₅ = (5 - 1)(5 - 2)(5 - 3) = 4 × 3 × 2 = 24 > 0 e.g., positive
Hence, after 3rd term all the terms of the sequence are positive.

ANSWER

Hiii guys.....How r u alll

Posted by ?Harshitha? Harshi 6 years, 2 months ago

CBSE > Class 10 > Mathematics

3 answers

?Harshitha? Harshi 6 years, 2 months ago

No

?Harshitha? Harshi 6 years, 2 months ago

Na

Sahil Singh 6 years, 2 months ago

New.....

ANSWER

-5 is one of the zeroes of 2x Square +px-15. Zeroes of p(x2+x) +k are equal to each other. Find the value of k.

Posted by Aaliya Yduvanshi.... 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Aaliya Yduvanshi.... 6 years, 2 months ago

Please give me answer

ANSWER

Find the zeroes of integers between 10 and 500 which are divisible by 7 ?

Posted by Aaliya Yduvanshi.... 6 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Aadya Singh ? 6 years, 2 months ago

So, the sum of integers between 10 and 500 is 17885.

Aadya Singh ? 6 years, 2 months ago

AP are : 14 , 21 , 28 ......497 . So, a= 14 , Tn = 497 , d= 7 . Now, Tn = a + (n-1) d => 497 = 14 +(n-1) 7 => n= 70 . Sn = n/2 ( Tn + a) => Sn = 70/2 ( 497+14) => Sn = 35× 511 => Sn = 17885 .

ANSWER

Solve for x and y : 37x+43y = 123. , 43x + 37y =117

Posted by Aaliya Yduvanshi.... 6 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Aadya Singh ? 6 years, 2 months ago

So, y= 2 and x= 1

Aadya Singh ? 6 years, 2 months ago

37x + 43y = 123...(1) , 43x + 37y = 117....(2) , Adding (1) and (2) , we get, 80x + 80y = 240 => x+y = 3.....(3) , Subtracting (2) from (1) , we get, -6x +6y = 6 => -x+y = 1 .....(4) . Adding (3) and (4) , we get, 2y= 4 => y = 2 . Now, put the value of y in (3) , we get, x = 1.

ANSWER

Find the middle term of an A. P 20,16,12...,-180

Posted by Aaliya Yduvanshi.... 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Aadya Singh ? 6 years, 2 months ago

Tn = a+(n-1)d => -180 = 20 + (n-1) -4 => -200 = -4n + 4 => -204 = -4n => n = 51 . Since, there are 51 terms. So, the middle term = 26 th term.

ANSWER

Check whether the following are quadratic equations (2x–1)(x–3)=(x+5(x–1)

Posted by Shivam Yadav 6 years, 2 months ago

CBSE > Class 10 > Mathematics

4 answers

Shivam Yadav 6 years, 2 months ago

Right answer

Shivam Yadav 6 years, 2 months ago

Yes

Yogita Ingle 6 years, 2 months ago

LHS: (2x–1)(x–3) =2x²–6x–x+3 = 2x²–7x+3

RHS: (x+5)(x–1) = x²–x+5x–5 = x²+ 4x – 5

Now; 2x²–7x+3 = x²+4x–5

Or, 2x²–7x+3–x2−4x+5 = 0

Or, x²–11x+8=0

Aadya Singh ? 6 years, 2 months ago

Yes, it is quadratic equation.

ANSWER

Prove that opposite side of a quadilateral circumscribing a circle subtend supplementary angle at the centre

Posted by Gautam Das 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Mohd Kadeer Khan 6 years, 2 months ago

Jhu

ANSWER

Sin + cos - tan chapter 8

Posted by Simrandeep Simrandeep 6 years, 2 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Sin + cos - tan

Posted by Simrandeep Simrandeep 6 years, 2 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

The radii of two concentric circle are 13 cm and 8 cm . AB is a diameter of the bigger circle. BD is a tangent to the smaller circle touching it at D . Find the length of AD

Posted by Naved Ahmad 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 2 months ago

From right triangle BOD

BD = √(OB²-OD²) = √(13²- 8²) = √105

from right triangle POD

PD = √(OP²-OD²) = √(13²-8²) = √105

PB = BD + PD = 2√105 PB²= 420

from right triangle APB

AP = √(AB²- PB²) =√26²- 420 = √676-420 = √256 = 16

ANSWER

Prove 3 root 5 is a rational number

Posted by Sahil Saharan 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Aadya Singh ? 6 years, 2 months ago

3√5 is a irrational number not rational number.

ANSWER

If alpha and beta are the zeros of a quadratic polynomial such that alpha + beta =24 and alpha - beta =8 find quadratic polynomial having Alpha and beta as its zeros

Posted by Kalpana Yadav 6 years, 2 months ago

CBSE > Class 10 > Mathematics

4 answers

Suhani Hotwani 6 years, 2 months ago

Alpha and beta are 2 zeros , so alpha + beta = 24 (equation…1) And, alpha - beta = 8 (equation…2) By elumination method, Alpha is 16 and beta is 8 Now putting in formula X*2-(alpha + beta ) +( aplha multiply by beta) We get, x*2 - 24x + 128 Solved!!!!!!!

Adarsh Singh 6 years, 2 months ago

aata na jaata jai bharat maata

Aadya Singh ? 6 years, 2 months ago

So, equation => x^2 - 24x + 128 = 0

Aadya Singh ? 6 years, 2 months ago

Alpha + beta = 24 .....(1) , alpha - beta = 8 .....(2) . Solving (1) and (2) , we get, alpha = 16 and beta = 8 . Then, equation is = x^2-(alpha + beta)x + alpha×beta = 0 => x^2- (16+8)x + 16×8 = 0 => x^2 - 24x + 128= 0 .

ANSWER

(cosA-sinA+1)/(cosA+sinA-1)=cosecA+cotA

Posted by Vishal Shakya 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 2 months ago

{tex}L H S=\frac{\cos A-\sin A+1}{\cos A+\sin A-1}{/tex}
{tex}=\frac{\sin A(\cos A-\sin A+1)}{\sin A(\cos A+\sin A-1)}{/tex}
{tex}=\frac{\sin A \cos A-\sin ^{2} A+\sin A}{\sin A(\cos A+\sin A-1)}{/tex}
{tex}=\frac{\sin A \cos A+\sin A-\left(1-\cos ^{2} A\right)}{\sin A(\cos A+\sin A-1)}{/tex}
{tex}=\frac{\sin A(\cos A+1)-(1-\cos A)(1+\cos A)}{\sin A(\cos A+\sin A-1)}{/tex}
{tex}=\frac{(1+\cos A)(\sin A+\cos A-1)}{\sin A(\cos A+\sin A-1)}{/tex}
{tex}=\frac{(1+\cos A)(\sin A+\cos A-1)}{\sin A(\cos A+\sin A-1)}{/tex}
{tex}=\frac{1}{\sin A}+\frac{\cos A}{\sin A}{/tex}
= cos A + cot A = RHS
Proved

ANSWER

Name the two early industries that developed in England

Posted by Manish Gupta 6 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Royal Pandit 6 years, 2 months ago

Happy Birthday Deepika ji

Shreya... #Be Positve Be Happy 6 years, 2 months ago

Textile industry, iron and steel industry.

ANSWER

Point P divides the line segment joining the points A(2,-5) and B(5,2) in the ratio 2:3. Name the quadrant in which P lies.

Posted by Khyati Agrawal 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Rohan Raj 6 years, 2 months ago

Hi khyati.

ANSWER

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that : AB +CD = AD+BC

Posted by Atulya Akchu 6 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Sia ? 6 years, 2 months ago

We know that the tangent segments from an external point to a circle are equal

{tex}\therefore{/tex} AP = AS ........(1)
BP = BQ .......(2)
CR = CQ .......(3)
DR = DS .......(4)
Adding (1), (2), (3) and (4), we get
(AP + BP) + (CR + DR) = (AS + BQ + CQ + DS)
{tex}\Rightarrow{/tex} AB + CD = (AS + DS) + (BQ + CQ)
{tex}\Rightarrow{/tex} AB + CD = AD + BC

Atulya Akchu 6 years, 2 months ago

Tq my dear frnd..... It helps me a lot..... ✌️?

ANSWER

Differences between polynomial & algebric expression

Posted by Akhi Sahai 4 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 4 years, 6 months ago

An algebraic expression, in which variable(s) does (do) not occur in the denominator, exponents of variable(s) are whole numbers and numerical coefficients of various terms are real numbers, is called a polynomial. (iii) Numerical coefficient of each term is a real number. x x are not polynomials.

ANSWER

How to learning the formula of Trigonometry

Posted by Mayank Tripathi 6 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Student Lyf ? 6 years, 2 months ago

By writing 5-6 times in notebook

Lakshay . 6 years, 2 months ago

Learn it

ANSWER

Prove that √5 is rational number

Posted by Nikhil Chauhan 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Hosila P Sharma 6 years, 2 months ago

It is not rational no.

ANSWER

Find the area of quadrilateral ABCD the co-ordinate of whose vertices are A(-3,2) B(-5,4) C(7,-6) D(-5,-4)

Posted by Karanjeet Behera 6 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Suhani Hotwani 6 years, 2 months ago

By dividing quadrilateral in 2 parts by joining daigonal from A to c , so it becomes 2 triangles 1. Triangle ABC 2. Triangle ACD Now , placing the point given in question Finally put the formula area of triangle Which is , ½ x1(y2-y3)+x2(y3-y1)+x3(y1-y3) So we get Area of triangle 1st is 2 cm Area of triangle 2nd is 38 cm Finally, Adding both the triangle area 2+38=40 cm Solved!!!!!!!!!!!!!!

Suhani Hotwani 6 years, 2 months ago

Area of quadrilateral is 40

ANSWER

Prove that sec theta

Posted by Karanjeet Behera 6 years, 2 months ago

CBSE > Class 10 > Mathematics

3 answers

Royal Pandit 6 years, 2 months ago

Happy Birthday Deepak ji

Nidhi?? Pandey?? 6 years, 2 months ago

What is the full question¿¿

Ad Singh 6 years, 2 months ago

Give complete questions

ANSWER

From a point p on the ground the angle of elevation of the top of a 10 in building is 30 degree apply step in fixed at the top of the building and the angle of elevation of the top of the flagstaff from the point p is 45 degree find the length of the flag staff and the distance of building from the point p (root 3 is equal to 1.73)

Posted by Karanjeet Behera 6 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Suhani Hotwani 6 years, 2 months ago

Its 7.32

Suhani Hotwani 6 years, 2 months ago

Distance is 17.32 cm And Length of Flagstaff is 7.3w

ANSWER

construct a right angle triangle ABC with ab is equal to 6 CM BC 8 cm and angle b is equal to 90 degree draw BD perpendicular from b on AC draw the circle through BCD and construct the tangents from a to the circle

Posted by Karanjeet Behera 6 years, 2 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Prove that a parallelogram circumscring a circle is a rhombus

Posted by Karanjeet Behera 6 years, 2 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Tan(90+a)=

Posted by Rishi David 6 years, 2 months ago

CBSE > Class 10 > Mathematics

4 answers

Suhani Hotwani 6 years, 2 months ago

Cot a

Royal Pandit 6 years, 2 months ago

Happy Birthday Deepika ji

Shreya... #Be Positve Be Happy 6 years, 2 months ago

Cot a

Navneet Keshri 6 years, 2 months ago

Cota

ANSWER

In the given figure,O is the centre of a circle and TP is the tangent to a circle from an external point T . If angle PBT =30°,prove that BA:AT=2:1

Posted by Jatin Pratap Singh 6 years, 2 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

What is the area of cuboid?

Posted by Rohan Raj 6 years, 2 months ago

CBSE > Class 10 > Mathematics

3 answers

Royal Pandit 6 years, 2 months ago

Happy Birthday Deepika ji

Secret Girl...??‍?? 6 years, 2 months ago

Right lucky... ??

?Lucky ? 6 years, 2 months ago

Total surface area of cuboid=2( lb+bh+hl )

ANSWER

THE SUM OF n TERMS OF THE AP IS 4n-n^2, FIND THE COMMON DIFFERENCE.

Posted by Shiri Sengar 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Aadya Singh ? 6 years, 2 months ago

Common difference = 1

ANSWER

What is 24 carat gold? How will you convert it into 18 carat gold?

Posted by ?Lucky ? 6 years, 2 months ago

CBSE > Class 10 > Mathematics

7 answers

Secret Girl...? 6 years, 2 months ago

My pleasure

?Lucky ? 6 years, 2 months ago

Thanks secret girl

Secret Girl...? 6 years, 2 months ago

I hope u got ur answer..... ☺

Secret Girl...? 6 years, 2 months ago

24 carat gold is pure gold. Pure gold is very soft and not suitable for making jewellery. Therefore, to increase it's hardness , it is alloyed either with copper or silver. 18 carat gold is prepared by alloying 18 parts pure gold with 6 parts of either cooper or silver.

Secret Girl...? 6 years, 2 months ago

Pure gold is defined as 24 carats or having a fineness.

Secret Girl...? 6 years, 2 months ago

24 carat gold means pure gold means 24 of 24parts of alloy is gold making it pure gold.

?Lucky ? 6 years, 2 months ago

This is a science ques.

ANSWER

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