Question

The sum of 2nd and 5th term of AP is 14 and their product is 40 find the sum of first 16 terms

Answer 1

here is the answer buddy

a+d=2ndterm
a+4d=3rd term

a+d+a+4d=14
2a+5d=14
2a=14-5d
a=(14-5d)/2

(a+d)(a+4d)=[{(14-5d)/2}+d][{(14-5d)/2}+4d]
={(14-5d+2d)/2}{(14-5d+8d)/2}
={(14-3d)(14+3d)}/4
=(196-8d²)/4=40
=196-d²=160
= d²=196-160
=d²=36
=d=6
2a+5d=14
2a+5(6)=14
2a=14-30
a=-16/2
a=-8

16th term=a+15d
=-8+15(6)
=90-8
=82
finally arrived
hope it helps