The sequence of s1, s2, s3, . . . , sn of n is such that sk = 2k -1 if

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

The sequence ofs1,s2,s3,...,sns1,s2,s3,...,sn of n is such thatsk=2k−1sk=2k−1if k is odd and sk=−sk−1sk=−sk−1 if k is even. Is the sum of the terms in the sequence positive?

(1) The sum of the first 11 terms in the sequence is positive.
(2) n is odd.


When you modify the original condition and the question, they become 1,-1,3,-3,5,-5,.... and sum of up to an odd-number term is always a positive number. However, in 2), since n=odd, sum until the term n is always positive, which is yes and sufficient.
Therefore, the answer is B.


 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.

Here B is sufficient as ODD value of N will give us a positive result which is a result of the other terms cancelling out..

From the stem, we can get the odd terms of the sequence is a positive odd number (eg: 2.1-1=1, 2.3-1=5) and the even terms are negative of its previous term. Either the sum can be 0 when n is even or can be equal to the last odd term of the sequence in case of n is negative.

1) no information about the number of terms. not sufficient

2) the sum will be positive as it will be equal to the last term of the sequence. sufficient.

B is the answer.

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