Question

If a1,a2,a3 represents first, second, third terms in A.P. if the first term is 2 and (a1 + a2 ) a3 is minimum then the common difference is?​

Answer 1

Answer:

d = -5/2

Step-by-step explanation:

If a1,a2,a3 represents first, second, third terms in A.P. if the first term is 2 and (a1 + a2 ) a3 is minimum then the common difference is?​

Let say d is common difference

first term = a1

Second term a2 = a1 + d

Third term a3 = a1 + 2d

a1 = 2

a2 = 2 + d

a3 = 2 + 2d

Min of  ( a1 + a2) a3

(2 + 2 + d)(2 + 2d)

= 2(4 + d)( 1 + d)

= 2(d² + 5d + 4)

d = - 5/2 ( - b/a  for ax² + bx + c) will give the minimum value

or we can differentiate

2d + 5 = 0

=> d = -5/2