The sum of the first two terms of an arithmetic progression is 18 and the sum of the first four terms is 52. Find the sum of the first eight terms.

Term no:       1,   2,   3,    4,   5,   6,  7,    8,
...

The series:  __, __, __, __, __, __, __, __,
...

.                 
/_18_/

.                 
/____52____/

From trial and
error,

the 1st term = 7

the
2nd term = 18-7=11

common difference is
11-7=4

(Counter check by adding 4 consecutively to get 4th
and 5th term to be 15 and 19 respectively.  It is confirmed that sum of first 4 terms is
52)

8th term = 7+ 4.(8-1) = 7+ 28 =
35

Sum of first 8 terms = 8/2 . (7 + 35) = 4 (42) =
168