Question

If the third term of G.P is 4 then the product of its first 5 terms

Answer 1

Answer:

1024

Step-by-step explanation:

let r be the ratio

and let a be first term

then the first five terms will be

a , ar , ar² , ar³ , ar⁴

product will be a⁵r¹⁰

(ar²)⁵

ar² is the third term and it equals 4 so,

4⁵

=1024

Answer 2

It is given that the third term of the GP is 4

We know that the general term of a geometric progression with first term "a" and common ratio r is Tn =arⁿ⁻¹

T₃ = ar³⁻¹

⇒ 4 = ar².... (1)

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

a x ar x ar² x ar³ x ar⁴

⇒ a⁵r¹⁰

⇒  (ar²)⁵

⇒ (4)⁵

⇒ 1024

Hence the product of first 5 terms is 1024.