Question

If a,2(a+5) and 2(4a-5)are in ap then find a

Answer 1

If a,2(a+5) and 2(4a-5) are in A.P. then, 2[2(a+5)]=a+[2(4a-5)] =>4a+20=a+8a-10 =>5a=30 =>a=6

Answer 2

The value of a is 6.

Given,

Three numbers a, 2(a+5), and 2(4a-5) are in A.P.

To Find,

The value of a.

Solution,

The condition for 3 numbers to be in A.P is that the value of their common difference must be equal, which means

2(a+5)-a = 2(4a-5)-2(a+5) = d (common difference)

So,

2a+10-a = 8a-10-2a-10

On solving this equation we will get the value of a.

a+10 = 6a-20

30 = 5a

a = 30/5

a = 6.

Hence, the value of a is 6.