**Solution:**

Given,

Common difference, d = 7

22^{nd} term, a_{22} = 149

The sum of the first 22 terms, S_{22} = ?

By the formula of the nth term,

a_{n} = a + (n − 1) d

a_{22} = a + (22 − 1) d

149 = a + 21 × 7

149 = a + 147

a = 2 = First term

The sum of n terms,

S_{n} = n /2( a + a_{n} )

S_{22} = 22/2 (2 + 149)

= 11 × 151

= 1661