Question

 If the third term of G.P. is P . Then , the product of the first five terms of G.P. is ​

Answer 1

Step-by-step explanation:

ANSWER

It is given that the third term of the G.P is 2.

We know that the general term of an geometric progression with first term a and common ratio r is T

n

=ar

n−1

, therefore,

T

3

=ar

3−1

⇒2=ar

2

......(1)

Now, consider the product of first five terms that is:

a×ar×ar

2

×ar

3

×ar

4

=a

2

r

10

=(ar

2

)

5

=(2)

5

(using(1))

=32

Hence the product of first 5 terms is 32.

Answer 2

Given:

The third term of G.P = P

To find:

The product of first five terms of G.P

Calculation:

Let the first term of the G.P is ‘a’ and the common ratio of the G.P be ‘r’. The third term of the G.P (ar²) is P

=> Product of first five terms of G.P = a(ar)(ar²)(ar³)(ar⁴)

                                                          = a⁵r¹⁰

                                                          = (ar²)⁵

                                                          = P⁵

The product of first five terms of the G.P is P⁵