Question

If $a_1 + a_2 + a_3 + \dots + a_n = 3(2^{n+1} - 2)$, for every $n \ge 1$, then $a_{11}$ equals

Accepted Answer

6144. $S_n = 3(2^{n+1} - 2)$. $a_{11} = S_{11} - S_{10} = 3(2^{12} - 2) - 3(2^{11} - 2) = 3(2^{12} - 2^{11}) = 3 \cdot 2^{11} = 3 \cdot 2048 = 6144$.

Finding a Specific Term from Sum of Series

Practise this under exam conditions