An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.

Given:

An A.P. consists of 60 terms. The first and the last terms are 7 and 125 respectively.
To do:

We have to find the 32nd term.
Solution:

Let $a$ be the first term and $d$ be the common difference.

 Number of terms $n=60$

First term $a_1=a=7$

Last term $a_n=a+(n-1)d$

Therefore,

$a_{60}=a+(60-1)d=125$

$125=7+59d$

$59d=125-7$

$59d=118$

$d=\frac{118}{59}$

$d=2$

32nd term $a_{32}=a+(32-1)d$

$=7+31(2)$

$=7+62$

$=69$

The 32nd term is 69.

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Updated on: 10-Oct-2022

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