Question

The 7th and 21st terms of an ap are 6 and -22 respectively. find the 26th term

Answer 1

Given:-
a7=6
a21=-22

Solution:-

a7=6

a+(7-1)d=6

a+6d=6..... . i


a21=-22

a+20d=-22.......ii

sub ii from i

a+6d-(a+20d)=6-(-22)

a+6d-a-20d=6+22

-14d=28

d=-2

putting value of d in equation i

a+6d=6

a+6×(-2)=6

a-12=6

a=6+12

a=18

now we have to find a26

a26=a+25d

a26=18+25×(-2)

a26=18-50

a26=-32

The 26th term is -32