Question

find the sum of frist 22terms in Ap in which d=17and 22nd term is 149

Answer 1

t22=a+21d
149=a+(21*17)
a =149-357
a= -208

now
sn=n(a+L)/2
s22=22(-208+149)/2
s22= 11×59=649

Answer 2

Number of terms = 22

Common difference = 17

Last term = 149.

First term = ? = -208

Sum of 22 terms = ? =  -649.

We have,

 Last term = First term + ( No. of terms - 1 ) Common difference

 149 = First term + ( 22 - 1 ) 17

 149 = First term + 21 x 17

149 = First term + 357

 First term = 149 - 357

 First term = - 208

Now,

 Sum of ' n ' terms  = No. of terms / 2 ( First term + Last term )
 
 Sum of 22 terms = 22 / 2 ( -208 + 149 )

                             = 11 ( -59 )

                            = -649.