A sequence (a_n) has first term a_1=1, and subsequent terms defined by a_{n+1}=l a_n for n \geq 1. What is the product of the first 15 terms of the sequence?

Oxford University MAT 2016 Solved Papers

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A sequence

(a_n)

has first term

a_1=1

, and subsequent terms defined by

a_{n+1}=l a_n

for

n ≥ 1

. What is the product of the first 15 terms of the sequence?

Solution:

Considering the sequence,

a_2=l, a_3=l^2, a_4=l^3

, each additional term multiplies the previous term by

l

. The product of the first 15 terms is equal to

l^{1+2+. . .+14}=l^{\;{14 * 15}/{2}}=l^{105}

. The answer is (d).

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