Question

Write the explicit rule of the arithmetic sequence that has a first term of 3 and a fourth term of 18

Answer 1

`a_(n)` = 5n - 2

Explanation:

The nth term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₄ = 18 , then

a₁ + 3d = 18 , that is

3 + 3d = 18 ( subtract 3 from both sides )

3d = 15 (divide both sides by 3 )

d = 5

Then

`a_(n)` = 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2 ← explicit rule