# 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.