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Question
Which term of A.P 3, 10, 17, .... Will be 84 more than its 13th term?
Solution
The given A.P is 3, 10, 17, ....
Here a = 3, and d = 10 - 3 = 7
Now
`t_13 = a + 12d = 3 + 12 xx 7 = 3 + 84 = 87`
Let the required term be nth term
`:. t_n - t_13 = 84`
=> [a + (n - 1)d] - 87 = 84
`=> 3 + (n - 1) xx 7 = 171`
`=> (n - 1) xx 7 = 168`
=> n - 1 = 24
=> n = 25
Thus required term = 25th term
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