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**Exercise 9.3**

**1. Find the 20 ^{th} and terms of the G.P. **

**Ans. **Here and

=

And = =

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

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

=

== 3072

**3. The 5 ^{th}, 8^{th} and 11^{th} 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 4 ^{th} term of a G.P. is square of its second term and the first term is Determine its 7^{th} 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, 13^{th} term of the given G.P. is 128.

**(b)** Here , and

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

**(c)** Here , and

Therefore, 9^{th} 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 7 ^{th} term 64, determine **

**Ans. **Given: = 729 and

when

=

= 2059

There no given all question

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