Question

An arithmetic progression has the 3rd term of 13 and the last term of 148. If the common difference is 5, find the number of terms of the progression.

Answer 1

30 terms

Explanation:

The n th term of an AP is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here d = 5 and a₃ = 13, thus

a₁ + 2d = 13

a₁ + 2(5) = 13

a₁ + 10 = 13 ( subtract 10 from both sides )

a₁ = 3

Thus

`a_(n)` = 3 + 5(n - 1) = 148 ( subtract 3 from both sides )

5(n - 1) = 145 ( divide both sides by 5 )

n - 1 = 29 ( add 1 to both sides )

n = 30

The progression has 30 terms