Question

Find the third term of the sequence where sum of $n$ terms is given as: $S_n=\frac{n^2(n+1{)}^2}{4}$

• A. $36$
• B. $27$
• C. $24$
• D. $54$

Answer 1

The correct option is B $27$

Here, the sum of $n$ terms of a sequence is given as $S_n=\frac{n^2(n+1{)}^2}{4}$
First term $=S_1=\frac{1^2(1+1{)}^2}{4}=1$
Second term $=S_2-S_1=\frac{2^2(2+1{)}^2}{4}-1=9-1=8$
Third term $=S_3-S_2=\frac{3^2(3+1{)}^2}{4}-\frac{2^2(2+1{)}^2}{4}=36-9=27$
Hence, the third term is $27$.