Question

if 5th term of a gp is 32 and common ratio 2 then the sum of 14th term is
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Answer 1

Answer:

S₁₄ = 2(2¹⁴-1)

Step-by-step explanation:

Given: Fifth term of G.P.=32, common ratio=2

Let the first term of G.P. be 'a'.

w.k.t., general term of a G.P. is aₙ = arⁿ⁻¹, where a is first term and r is common ratio.

⇒ Fifth term of G.P., a₅ = ar⁴ = a.2⁴ = 16a

⇒ 16a = 32

or a = 32/16

or a = 2

w.k.t., sum of n terms of a G.P. is Sₙ = a(rⁿ-1)/(r-1).

⇒ Sum of 14 terms, S₁₄ = 2(2¹⁴-1)/(2-1)

or S₁₄ = 2(2¹⁴-1)

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