The third term of a GP is 3. What is the product of its first five terms?

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NDA (Held On: 18 Apr 2021) Maths Previous Year paper

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Answer 1

Concept:

Let us consider sequence a₁, a₂, a₃ …. a_n is a G.P.

Common ratio = r = \(\rm a_2\over a_1 \) = \(\rm a_3\over a_2 \) = \(\rm a_n\over a_{n-1} \)

Calculation:

Consider,

(a = 3) be the 3^rd term of the G.P series,

So, we can write the five terms as,

\(\rm a\over r^2\), \(\rm a\over r\), a, ar, ar²

So, the product of the five terms (P) will be,

P = \(\rm a\over r^2\) × \(\rm a\over r\) × a × ar × ar2 = a⁵

Since,

a = 3,

∴ The product of the first five terms (P) = 3⁵ = 243