Question

Write an explicit formula for the sequence. Use this, to find the 80th term of the sequence that begins: -3,1,5,9....

Answer 1

see explanation

Explanation:

There is a common difference d between consecutive terms in the sequence, that is

9 - 5 = 5 - 1 = 1 - (- 3) = 4

This indicates the sequence is arithmetic with n th term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 3 and d = 4, thus

`a_(n)` = - 3 + 4(n - 1) = - 3 + 4n - 4 = 4n - 7 ← explicit formula

Thus

`a_(80)` = 4(80) - 7 = 320 - 7 = 313