Question

Write an explicit formula for the sequence

Answer 1

`u_(n)` = - 5.6n + 3.2

Explanation:

The explicit formula for an arithmetic sequence is

`u_(n)` = u₁ + (n - 1)d

where u₁ is the first term and d the common difference

To find u₁ use the given recursive formula

u₁ = u₀ - 5.6 = 3.2 - 5.6 = - 2.4

from the recursive formula d = - 5.6 , then explicit formula is

`u_(n)` = - 2.4 - 5.6(n - 1) = - 2.4 - 5.6n + 5.6 = - 5.6n + 3.2