Question

write a recursive formula for $a_n$, the $n^{\text{th}}$ term of the sequence 19, 11, 3, $-5$,....
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 19, so $a_1 = 19$.

Step2: Find common difference

Calculate the difference between consecutive terms: $11-19=-8$, $3-11=-8$, $-5-3=-8$. The common difference is $-8$.

Step3: Write recursive formula

For a recursive formula, each term is the previous term plus the common difference. So $a_n = a_{n-1} - 8$ for $n\geq2$.

Answer:

$a_1 = 19$
$a_n = a_{n-1} - 8$ (for $n \geq 2$)