Question

Write a recursive formula for an, the nthterm of the sequence 8, -2, -12, ....

Answer 1

We have the sequence: 8, -2, -12...

We can prove that this is an arithmetic sequence as there is a common difference d=-10 between consecutive terms.

Then, the recursive formula (the expression where the value of a term depends on the value of the previous term) can be written as:

$a_n=a_{n-1}-10$

Answer: the recursive formula is a1 = 8, a(n) = a(n-1) - 10