How many terms are there in the AP
Question:

How many terms are there in the AP $11,18,25,32,39, \ldots .207 ?$

Solution:

To Find: we need to find a number of terms in the given AP.

Given: The series is $11,18,25,32,39, \ldots 207$

$a_{1}=11, a_{2}=18, d=18-11=7$ and $a_{n}=207$

(Where $a=a_{1}$ is first term, $a_{2}$ is second term, $a_{n}$ is nth term and $d$ is common difference of given $\mathrm{AP}$ )

Formula Used: $a_{n}=a+(n-1) d$

$a_{n}=207=a_{1}+(n-1)(7)$

$207-11=(n-1)(7)$ [subtract 11 on both sides]

$196=(n-1)(7)$

$28=(n-1)$ [Divide both side by 7 ]

$\mathrm{n}=29$ [add 1 on both sides]

So there are 29 terms in this AP.