Question

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

Answer 1

In the given problem, let us first find the 13^th term of the given A.P.

A.P. is 3, 10, 17 …

Here

First term (a) = 3

Common difference of the A.P. (d) = 10 - 3 = 7

Now, as we know,

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

So for 12th term (n = 13)

`a_13 = 3 + (13 - 1)(7)`

= 3 + 2(7)

= 3 + 84

= 87

Let us take the term which is 84 more than the 13^th term as a_n. So,

`a_n = 84 + a_13`

= 84 + 87

= 171

Also `a_n = a + (n -1)d`

171 = 3 + (n - 1)7

171 = 3 + 7n - 7

171 = -4 + 7n

171 + 4 = 7n

Further simplifying, we get,

175 = 7n

`n = 175/7`

n = 25

Therefore the 25 th term of the given A.P is  84 more than the 13^th term