An AP has 4 as its first term. what is the common difference if the sum of the first 12 terms is 2 times the sum of the first 8 terms.
The sum of the first n terms of an AP with first term a and common difference d is equal to `S_n = (n/2)*(2a +(n-1)*d)` .
It is given that the first term of the AP is 4, and the sum of the first 12 terms is 2 times the sum of the first 8 terms.
This gives 6(8 + 11*d) = 2*4*(8 + 7*d)
=> 48 + 66d = 64 + 56d
=> 10d = 16
=> d = 1.6
The common difference of the AP is 1.6