Question

PLEASE HELP


b(1)=−500

b(n)=b(n−1)⋅

5

4

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What is the 3^{\text{rd}}3

rd

3, start superscript, start text, r, d, end text, end superscript term in the sequence?

Answer 1

Answer: $3^{rd}$ term of the given sequence is -320.

Step-by-step explanation:

Given sequence : $b(n)=b(n-1)\cdot\dfrac{4}{5}$ ,  b(1)=−500

For n =2,

$b(2) =b(1)\cdot\dfrac45=-500\cdot \dfrac45\\\\=-100\cdot4\\\\=-400$

For n = 3

$b(3) =b(2)\cdot\dfrac45=-400\cdot \dfrac45\\\\=-80\cdot4\\\\=-320$

So, $3^{rd}$ term of the given sequence is -320.