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...
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.