Question

if the common difference of the ap in which T7=9 and T1T2T7 is least ,is d then 20d is

Answer 1

First term =a
Common difference= d
T7= a+6d = 9
a= 9-6d
now,
T1T2T7=a*(a+d)*(a+6d)
=(9-6d)*(9-5d)*9
=(81-45d-54d+30d^2)*9
=9*(30 d^2 -99d +81)
=9*3*(10 d^2 -33d +27)
It is least therefore differentiate it with respect to d and then equate it to zero.
On differentiating
9*3*(20d-33)=0
20d = 33 Ans.