Progressions

Here, 7-2 = 5
12-7 = 5
17- 12 = 5, so given is Arithmetic progression with first term, a=2 and d= 5, we have given S (sum)= 156 and last term, l = x.

From equation, S = n/2 (a + l)
156 = n/2 (a + a + (n-1)d)
156 = n/2 (2a+nd – d)
312 = n (4+ 5n – 5)
that gives, 312 = 5n^2 – n
5n^2 – n- 512 =0.
5n^2 -40n + 39n -512 =0
(5N+39) (N-8) =0
So, n = 8.

putting value of n,
x = 2 + (8-1)*5
x= 2+35
x= 37.