Let the first term be taken as a.
Given,
a22 = 149 and the common difference d = 22
Also, we know that
an = a + ( n – 1) d
So, the 22nd term is given by
a22 = a + (22 – 1)d
149 = a + (21) (22)
a = 149 – 462
a = – 313
Now, for the sum of term
Sn = \(\frac{n}{2}\)[2a + (n − 1)d]
Here, n = 22
S22 = \(\frac{22}{2}\)[2(−313) + (22 − 1)(22)]
= (11)[ – 626 + 462]
= (11)[–164]
= – 1804
Hence, the sum of first 22 terms for the given A.P. is S22 = -1804