Question

Write an
explicit formula for An, the nth term of the sequence 15, 8, 1, ....

Answer 1

`a_(n)` = 22 - 7n

Explanation:

There is a common difference d between consecutive terms, that is

8 - 15 = 1 - 8 = - 7

This indicates the sequence is arithmetic with explicit formula

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 15 and d = - 7 , then

`a_(n)` = 15 - 7(n - 1) = 15 - 7n + 7 = 22 - 7n ← explicit formula

Answer 2

b(n) = 15 - 7(n - 1)

Explanation:

15 is the y-intercept

-7 is the slope