Question

Given sum of the first $n$ terms of an $A.P.$ is $2n + 3n^2$. Another $A.P.$ is formed with the same first term and double of the common difference, the sum of n terms of the new $A.P.$ is:

• A. $n+4n^2$
• B. $6n^2 - n$
• C. $n^2+4n$
• D. $3n+2n^2$

Answer 1

Answer: (B)

Given $S_n = 2n + 3n^2$M
Now, first term $= 2 + 3 = 5$
second term $= 2(2) + 3(4) = 16$
third term $=2(3)+3 (9) = 33$
Now, sum given in option only has the same first term and difference between 2nd and 1st term is double also.