Question

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

Answer 1

In the given problem we need to find the 32 nd term of an A.P which contains a total of 60 terms

Here we are given the following

First term (a) = 7

Last term (`a_n`) = 125

Number of terms (n) = 60

So, let us take the common difference as d

Now as we know

So for the last term,

125 = 7  + (60 - 1)d

125 = 7 + (59)d

125 - 7 = 59d

118 = 59d

Furthur simplifying

`d = 118/59`

d= 2

So for the 32 nd term (n = 32)

`a_32 = 7 + (32 - 1)2`

= 7 + (31)2

= 7 + 62

= 69

Therefore the 32^nd term of the given A.P. is 69