Question

Given a1 = 5 and an = an-1 + 4, find the explicit formula

Answer 1

The formula explicit formula is: aₙ = 4n + 1

How to find the area explicit formula?

We are given that:

a₁ = 5

aₙ = aₙ ₋ ₁ + 4

Thus;

a₂ = a₂ ₋ ₁ + 4

a₂ = 5 + 4

We know that the general formula for the nth term of an arithmetic progression is;

aₙ = a + (n - 1)d

Where;

a is first term

d is common difference

Thus, we have;

aₙ = 5 + (n - 1)4

aₙ = 4n + 1