SECTION B: DATA INTERPRETATION AND QUANTITIATIVE ABILITY

54. Consider a sequence –6, –12, 18, 24, –30, –36, 42,…..if sum of the first n terms of the sequence is 132, then the value of n is ______ ?

(A) 11 (B) 13 (C) 18 (D) 24 (E) 22

Solution:

The given sequence is –6, –12, 18, 24, –30, –36, 42, …………

The first two terms are negative and the next two terms are positive and so on, with terms being consecutive multiples of 6.

The sum of the first 4 terms is 24. Similarly the sum of the next 4 terms is also 24 and it is repeated in the same way.

The sum of first 20 (5 sets of 4 numbers each) terms is 24 ´ 5 = 120.

The 21^st term = –126

22^nd term = –132.

23^rd term = +138

24^th term = +144

\ The sum of first 21 terms = –6,

the sum of first 22 terms = –138,

the sum of first 33 terms = –138 + 138 = 0 and the sum of first 24 terms = 0+ 144 = 144

We can observe that sum to (4n + 1) terms or (4n + 2) terms is negative.

The sum to (4n + 3) terms is 0.

The sum of 4n terms is a multiple of 24.

132 cannot fit into any of these categories.

\ The value of n does not exist for S_n = 132. (Ignore)