Question

which term of A.P 3,10,17......….... . Will be 84 more than its 13 term

Answer 1

a = 3

d= 7

a13 = a + 12d

= 3 + 84

= 87

hence, 87+ 84

= 171

an= 3 + 7n -7

171 = 7n - 4

7n = 175

n = 25

Answer 2

a=3

d=10-3=7

$13th \: term \: = a + (n - 1)d \\ = 3 + (13 - 1)7 \\ = 3 + 12 \times 7 \\ = 3 + 84 \\ = 87$
let the nth term be 84 more than the 13 th term.

So , nth term of AP =87+84
${n}^{th} \: term \: = 171 \\ a + (n - 1)d = 171 \\ 3 + (n - 1)7 = 171 \\ (n - 1) \times 7 = 171 - 3 \\ (n - 1)7 = 168 \\ (n - 1) = \frac{168}{7} \\ (n - 1) = 24 \\ n \: \: = 24 + 1 \\ n = 25$
So 25 th term of AP is 84 more than the 13 th term.