NCERT Solutions class-11 Maths Exercise 9.3 Part-1

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Exercise 9.3

1. Find the 20th and terms of the G.P.

Ans. Here and

=

And = =


2. Find the 12th term of a G.P. whose 8th term is 192 and the common ratio if 2.

Ans. Let be the first term of given G.P. Here and

=

== 3072


3. The 5th, 8th and 11th terms of a G.P. are and respectively. Show that

Ans. Let be the first term and be the common ratio of given G.P.

……….(i)

……….(ii)

……….(iii)

Squaring both sides of eq. (ii), we get

[From eq. (i) and (iii)]


4. The 4th term of a G.P. is square of its second term and the first term is Determine its 7th term.

Ans. Let be the common ratio of given G.P. Here and

Now,

=


5. Which term of the following sequences:

(a) is 128?

(b) is 729?

(c) is

Ans. (a) Here , and

Therefore, 13th term of the given G.P. is 128.

(b) Here , and

Therefore, 12th term of the given G.P. is 729.

(c) Here , and

Therefore, 9th term of the given G.P. is


6. For what values of the numbers are in G.P.?

Ans. Given: are in G.P.


Find the sum to indicated number of terms in each of the geometric progression in Exercises 7 to 10:

7. 0.15, 0.015, 0.0015, ………. 20 terms

Ans. Here, and

when


8. terms

Ans. Here, and

when


9. terms (if )

Ans. Here, and

when


10. terms (if )

Ans. Here, and

when


11. Evaluate:

Ans. Given:

=

=

= ……….(i)

Here in G.P.

and

Putting the value of in eq. (i), we get


12. The sum of first three terms of a G.P. is and their product is 1. Find the common ratio and the terms.

Ans. Let be first three terms of the given G.P.

According to question, ……….(i)

And

Putting value of in eq. (i),

Taking = and Taking =

When then first three terms are

When then first three terms are


13. How many terms of G.P. are needed to give the sum 120 ?

Ans. Here, and

when

Therefore, the sum of 4 terms of the given G.P. is 120.


14. The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum of terms of the G.P.

NA. Let be the first term and be the common ratio of given G.P.

……….(i)

And

………(ii)

Putting the value from eq. (i) into eq. (ii), we get

Putting value of in eq. (i), we get

when

=


15. Given a G.P. with = 729 and 7th term 64, determine

Ans. Given: = 729 and

when

=

= 2059


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