Question

Express the terms of the following sequence by glving an explicit formula

2, -2, -6, -10, –14,...

Answer 1

`a_(n)` = - 4n + 6

Explanation:

There is a common difference between consecutive terms of the sequence

- 2 - 2 = - 6 - (- 2) = - 10 - (- 6) = - 14 - (- 10) = - 4

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 = 2 and d = - 4 , then

`a_(n)` = 2 - 4(n - 1) = 2 - 4n + 4 = - 4n + 6