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Question 18
If $$a_1 + a_2 + a_3 + .... + a_n = 3(2^{n + 1} - 2)$$, for every $$n \geq 1$$, then $$a_{11}$$ equals
Correct Answer: 6144
Solution
11th term of series = $$a_{11}$$ = Sum of 11 terms - Sum of 10 terms = $$3(2^{11 + 1} - 2)$$-3$$(2^{10 + 1} - 2)$$
= 3$$(2^{12} - 2-2^{11} +2)$$=3$$(2^{11})(2-1)$$= 3*$$2^{11}$$ = 6144
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I tried an alternate method, trying to find the last term by deriving the first term of the series... Where have I possibly gone wrong in this approach?
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