Question

If a_1=9a
1
​
=9 and a_n=-3a_{n-1}a
n
​
=−3a
n−1
​
then find the value of a_5a
5
​
.

Answer 1

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The value of a₅ is -729.

What is geometrical series?

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.

Given the value of a₁=9 and the value of $a_n=-3a_{(n-1)}$. Therefore, the value of a₅ can be written as,

a₂ = -3(a₁) = -3(9) = -27

a₃ = -3(a₂) = -3(-27) = 81

a₄ = -3(a₃) = -3(81) = -243

a₅ = -3(a₄) = -3(-243) = -729

Hence, the value of a₅ is -729.

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