Question

Find the 97th term of the arithmetic sequence −16,2,20, ........

Answer 1

a₉₇ = 1712

Explanation:

there is a common difference between consecutive terms, that is

2 - (- 16) = 20 - 2 = 18

this indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + (n - 1)d

a₁ is the first term, d the common difference, n the term number

here a₁ = - 16 , d = 18 and n = 97

substitute these values into the nth term formula

a₉₇ = - 16 + (96 × 18) = - 16 + 1728 = 1712