Question

find the sum of 51 terms of an AP whose 2nd term is 2 and 4th term is 8

Answer 1

2nd term =2
4th term =8
a+(n-1)d=2 ,a+(2-1)d=2. ,a+d=2 equation 1
a+(n-1)d=8 , a+(4-1)d= 8. ,a+3d= 8. equation 2

subtract equation 2 from equation 1

a+3d=8
a+d= 2
- - -
2d=6 ,d=3 equation 3
putting equation 3 in eq 1

a+d=2
a+3=2
a=-1


51th term = a+(n-1)d
= (-1) +(51-1)*3
=-1+ 150
149