Question

Write an
explicit formula for the sequence 8, 6, 4, 2, 0, ... Then find a 14.
.

Answer 1

see explanation

Explanation:

there is a common difference between consecutive terms , that is

6 - 8 = 4 - 6 = 2 - 4 = 0 - 2 = - 2

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 = 8 and d = - 2 , then

`a_(n)` = 8 - 2(n - 1) = 8 - 2n + 2 = - 2n + 10

then

a₁₄ = - 2(14) + 10 = - 28 + 10 = - 18