Question

Which term of A.P 3, 10, 17, .... Will be 84 more than its 13th term?

Answer 1

The given A.P is 3, 10, 17, ....

Here a = 3, and d = 10 - 3 = 7

Now

${\displaystyle t_{13}=a+12d=3+12\times 7=3+84=87}$

Let the required term be nth term

${\displaystyle \therefore t_n-t_{13}=84}$

=> [a + (n - 1)d] - 87 = 84

${\displaystyle \Rightarrow 3+(n-1)\times 7 =171}$

${\displaystyle \Rightarrow (n-1)\times 7 =168}$

=> n - 1 = 24

=> n = 25

Thus required term = 25^th term