Question

Which term of the A. P. 3, 10, 17, ......... will be 84 more than its ${13}^{th}$ term ?

Answer 1

a = 3, d = 7

13th term will be,

$a_{13}$ = a + 12d

$a_{13}$ = 3 + 12$\times$7

$a_{13}$ = 3 + 84 = 87

Since, 84 more than its 13th term, so, value of term will be = 87 + 84 = 171

Now using ,

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

171 = 3 + 7n - 7

171 + 4 = 7n

$\frac{175}{7}$ = n

n = 25

So 25th term will be 84 more than its 13th term,

Verification:-

$a_{25}$ = a + 24 d

$a_{25}$ = 3 + 24$\times$7

$a_{25}$ = 3 + 168 = 171