How many terms are there in the AP 7, 11,15, …, 139?
In the given AP,
First term, a = 7
Common difference, a2 – a1 = (11 – 7) = 4
Let the no of terms be n
Nth term, an = 139
We know that, For any AP
an = a + (n – 1)d
where,
an = nth term
d = common difference
n = no of terms
using the above formula for given AP, we have
139 = 7 + (n – 1)(4)
⇒ 4(n – 1) = 132
⇒ n – 1 = 33
⇒ n = 34
Hence, there are 34 terms in given AP.