Answer:
30 terms
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = 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
[tex]a_{n}[/tex] = 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
