Question

If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.

Answer 1

Here, we are given two A.P. sequences whose n^th terms are equal. We need to find n.

So let us first find the n^th term for both the A.P.

First A.P. is 9, 7, 5 …

Here,

First term (a) = 9

Common difference of the A.P. (d)

Now, as we know,

So, for n^th term,

Second A.P. is 15, 12, 9 …

Here,

First term (a) = 15

Common difference of the A.P. (d)

Now, as we know,

So, for n^th term,

Now, we are given that the n^th terms for both the A.P. sequences are equal, we equate (1) and (2),

Therefore,