I'm working on the following problem:

An arithmetic progression has 14 terms. The sum of the odd-numbered terms is 140 and the sum of the even-numbered terms is 161. Find the common difference of the progression and the 14th term.

Here's what I've done with it so far...

A.P.

n = 14

T_1 + T_3 + T_5 + . . . + T_13 = 140

T_2 + T_4 + T_6 + . . . + T_14 = 161

T_1 + T_2 + . . . + T_14 = 140 + 161 = 301 = S_14

Now, for an A.P.,

S_n = n / 2 [ 2 * a + (n - 1) * d ]

S_14 = 14 / 2 [ 2 * a + (14 - 1) * d ] = 301

7 [ 2a + 13d ] = 301

2a + 13d = 43 . . . . . . (i)

So, I get one equation... Now, I need another equation in terms of a and d so that I can solve them simultaneously to find a and d and then the remaining question will be done...

Any help will be greatly appreciated.

Thanks,

Shahz.