The third term of GP is 4. Find the product of its first 5 terms ?

Question

Question

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Airforce Group X MBT 15-Jul-2021 Shift 1

Answer 1

Concept:

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

Common ratio = r = \(\frac{{{{\rm{a}}_2}}}{{{{\rm{a}}_1}}} = \frac{{{{\rm{a}}_3}}}{{{{\rm{a}}_2}}} = \ldots = \frac{{{{\rm{a}}_{\rm{n}}}}}{{{{\rm{a}}_{{\rm{n}} - 1}}}}\)
nth term of the G.P. is an = arn−1

Calculation:

Given: Third term of GP = 4

So, a₃= ar² = 4

Now, product of five time term is given by = a × ar × ar² × ar³ ×ar⁴

= a⁵r¹⁰

= (ar²)⁵

= 4⁵