There is a difference of 8 between consecutive terms:
6 = 6
6 + 8 = 14
6 + 8 + 8 = 22
6 + 8 + 8 + 8 = 30
and so on. The n'th term of the progression is then 6 + 8(n - 1). This means the last term is 180th in the sequence, since
1438 = 6 + 8(n - 1) ==> 1432 = 8(n - 1) ==> 179 = n - 1 ==> n = 180
Let S be the sum of the series,
S = 6 + 14 + 22 + 30 + ... + 1438
Reversing the series, we have
S = 1438 + 1430 + 1422 + 1414 + ... + 6
Adding together terms in the same position gives
2S = (6 + 1438) + (14 + 1430) + (22 + 1422) + ... + (1438 + 6)
2S = 1444 + 1444 + 1444 + ... + 1444
We know there are 180 terms in the progression, so there are 180 copies of 1444 on the right side,
2S = 180 * 1444 ==> S = (180 * 1444)/ 2
and so the sum is S = 129,960.
