Mathematics

Problem

Suppose

a_1, a_2, \dots, a_n, \dots

be an arithmetic progression of natural numbers. If the ratio of the sum of first five terms to the sum of first nine terms of the progression is

5:17

and

110 < a_{15} < 120

, then the sum of the first ten terms of the progression is equal to (a) 290 (b) 380 (c) 460 (d) 510