Question

Write an explicit formula for the recursive formula

A(n) = A(n - 1) + 3; A(1) = 6

Answer 1

`a_(n)` = 3n + 3

Explanation:

The sequence is arithmetic with explicit formula

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

From the recursive formula

a₁ = 6 and d = 3 [ the constant being added to A(n - 1) ] , then

`a_(n)` = 6 + 3(n - 1) = 6 + 3n - 3 = 3n + 3