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