Question

The Third term of G.P is 10. Then the product of first five terms is
1000
10000
100
100000
​

Answer 1

Answer:

10^5= 100000

Step-by-step explanation:

let first term be a/r^2

second - a/r

third- a

fourth- ar

fifth- ar^2

We do this so that the first and last term cancel out their common ratio r.

In this type of question always take the middle term a and on right side multiply by r and on left divide by r.

So 3rd term => a=10

Product of first five terms=

a/r^2 × a/r × a × ar ×ar^2

= a^5 [all r cancel out] we know a is 10

=> 10^5

=>(D)

Hope it helps...

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Answer 2

Given:

The third term of G.P = 10

To find:

The product of the first five terms

Calculation:

The general sequence of geometric progression having the first term 'a' and common ratio 'r' is a, ar, ar², ar³, ar⁴, ar⁵, ar⁶, ar⁷,........

=> Third term = 10

=> ar² = 10

=> Product of first 5 terms = a×ar×ar²×ar³×ar⁴

                                            = a⁵r¹⁰

                                            = (ar²)⁵  =  10⁵  = 100000

The product of the first five terms is 100000