Finding a Specific Term from Sum of Series

CAT 2019 Slot 1 · Quantitative Ability · Medium · Progressions

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

Answer

6144

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

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