Question

write a recursive formula for $a_n$, the $n^{\text{th}}$ term of the sequence $80, -20, 5, ....$

answer attempt 1 out of 2

$a_1 = \square$

$a_n = \square$

submit answer $a_{n - 1}$

Explanation:

Step1: Identify first term

The first term of the sequence is given as 80, so $a_1 = 80$.

Step2: Find common ratio

Calculate the ratio between consecutive terms:
$\frac{-20}{80} = -\frac{1}{4}$, $\frac{5}{-20} = -\frac{1}{4}$

Step3: Write recursive formula

Each term is $-\frac{1}{4}$ times the previous term, so for $n>1$, $a_n = -\frac{1}{4}a_{n-1}$.

Answer:

$a_1 = 80$
$a_n = -\frac{1}{4}a_{n-1}$ for $n > 1$