how to prove the sum of …

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Install Now

how to prove the sum of first terms of ap is 42 10th term to its 30th terms is 1:3 find the first term

Posted by Rohit Singh 7 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Naveen Sharma 7 years, 3 months ago

Ans.

Let first term of AP is a and comman difference is d.

as we know

$a_{n} = a + (n - 1) d w h e r e a_{n} i s n^{t h} t e r m$

=> $a_{10} = a + (10 - 1) d$

=> $a_{10} = a + 9 d$

And $a_{30} = a + (30 - 1) d$

=> $a_{30} = a + 29 d$

According to Question

=> $\frac{a + 9 d}{a + 29 d} = \frac{1}{3}$

=> 3a + 27d = a + 29d

=> 2a = 2d

=> a = d ............. (1)

Sum of first 6 terms = 42

We know

$S_{n} = \frac{n}{2} \times (2 a + (n - 1) d)$

=> $S_{6} = \frac{6}{2} \times (2 a + (6 - 1) d)$

=> $42 = 3 (2 a + 5 a)$

=> $42 = 21 a$

=> a = 2

First term is 2. Common difference is 2.

=> $a_{13} = 2 + (13 - 1) 2$

= > $a_{13} = 2 + 24$

=> $a_{13} = 26$

0Thank You

ANSWER

Related Questions

If alpha and beta are the zeros of the polynomial 2x²-5x+7, then find the value of alpha-¹+ beta-¹

Posted by Sandhya Vishwakarma 19 hours ago

CBSE > Class 10 > Mathematics

0 answers

Which I TEAM ARE YOU SUPPORTING

Posted by Aryan Agrawal 2 days, 11 hours ago

CBSE > Class 10 > Mathematics

2 answers

Prove √2-5as irrational

Posted by Aayush Yadav 2 days, 10 hours ago

CBSE > Class 10 > Mathematics

0 answers

6 men and 10 women can finish making pots in 8 days ,while the 4 men and 6 women can finish it in 12 days find the time taken by the one man alone from that of one women alone to finish the work

Posted by Kowsiga Rajkumar 1 day, 10 hours ago

CBSE > Class 10 > Mathematics

1 answers

7+7+√7

Posted by Raunak Kumar 21 hours ago

CBSE > Class 10 > Mathematics

1 answers

Ch 3 ex 3.3

Posted by Rohan Dhiman 12 hours ago

CBSE > Class 10 > Mathematics

1 answers

3.11stques

Posted by Paru Devi Ninama Ninama 19 hours ago

CBSE > Class 10 > Mathematics

0 answers

If the product of zeroes of polynomial ax²-6x-6 is 4. Find the value of a.

Posted by Bhavya Bansal 2 days, 13 hours ago

CBSE > Class 10 > Mathematics

1 answers

Solve the following system of linear equations 7x - 2y = 5 and 8x + 7y = 15 and verify your answer

Posted by Sakshi Bhalshankar 1 day, 15 hours ago

CBSE > Class 10 > Mathematics

0 answers

a+b ka hool square

Posted by Rajan Dubey 14 hours ago

CBSE > Class 10 > Mathematics

1 answers

myCBSEguide

CBSE, JEE, NEET, CUET

myCBSEguide

Test Generator

CUET Mock Tests

Download myCBSEguide App

All Courses

Other Websites

CBSE Courses

Resources

Corporate

NCERT Solutions

CBSE Sample Papers