Question

which term of the ap 3,10,17..will be more than its 13th term

Answer 1

It is clear that in this Ap the common difference is positive. It means all the terms will be in increasing order.

So all the terms after the 13th term will be greater than 13th term.

Answer 2

if you are asking for more than 84-
A = 3

d = 7 ,

13th term will be ,

xa13 = a + 12d

a13 = 3 + 12×7

a13 = 3+ 84 = 87

Since , 84 more than its 13th term ,so ,

value of term will be = 87 + 84 = 171

So value of term is 171

Now using ,

an = a+(n-1)d

171 = 3 + 7n - 7

171 + 4 = 7n

175/7 = n

n = 25 ,

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

Verification :-

a25 = a + 24 d

a25 = 3 + 24×7

a25 = 3 + 168 = 171