Question

Find an explicit formula for the following sequence, an, which starts with a1=8.
8,2,−4,−10,−16,…

Answer 1

Answer:

$a_{n}$ = 14 - 6n

Step-by-step explanation:

Note there is a common difference d between consecutive terms

2 - 8 = - 4 - 2 = - 10 - (- 4) = - 16 - (- 10) = - 6

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 = 8 and d = - 6, thus

$a_{n}$ = 8 - 6(n - 1) = 8 - 6n + 6 = 14 - 6n