Question:
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find the 32nd term.
Solution:
In the given problem, we need to find the 32nd term of an A.P. which contains a total of 60 terms.
Here we are given the following,
First term (a) = 7
Last term (an) = 125
Number of terms (n) = 60
So, let us take the common difference as d
Now, as we know,
$a_{n}=a+(n-1) d$
So, for the last term,
$125=7+(60-1) d$
$125=7+(59) d$
$125-7=59 d$
$118=59 d$
Further simplifying,
$d=\frac{118}{59}$
$d=2$
So, for the 32nd term (n = 32)
$a_{32}=7+(32-1) 2$
$=7+(31) 2$
$=7+62$
$=69$
Therefore, the $32^{\text {nd }}$ term of the given A.P. is 69 .