Question

The sum of first n terms of an AP is (3n^2+6n) . The common difference of the AP Is what ?

Answer 1

Sum of first n terms = 3n^2+6n

Sum of 1 term(or first term) (S1)= 3×1^2 + 6×1 = 9

Sum of first 2 term (S2)= 3×2^2 + 6×2 = 24
second term = S2 - S1 = 24 - 9 = 15

first term = 9
second term = 15
common difference = 15 - 9 = 6

Common difference is 6.

Answer 2

Given ,
Sum of first n terms = 3n²+6n

From this ,

Sum of first 1 terms = First term = 3(1²)+6(1)=9

Sum of first 2 terms = 3(2²)+6(2)=12+12=24


From this ,First term = 9 .

Second term = 24 - 9 = 15


Now Common difference = 15 - 9 = 6 .