2013Progression (Sequence and Series)Hard
Question
Let 
Then Sn can take value(s)
Then Sn can take value(s)Options
A.1056
B.1088
C.1120
D.1332
Solution
Sn = -12 - 22 + 32 + 42 - 52 - 62 + 72 + 82 .........
Sn = (32 - 12) + (42 - 22) + ............
Sn = 2(1 + 2 + 3 +........ + 4n)
Sn = 4n(4n + 1)
Sn = 4n(4n + 1) = 1056 is possible when n = 8
4n (4n + 1) = 1088 not possible
4n(4n + 1) = 1120 not possible
4n(4n + 1) = 1332 possible when n = 9.
Sn = (32 - 12) + (42 - 22) + ............
Sn = 2(1 + 2 + 3 +........ + 4n)
Sn = 4n(4n + 1)
Sn = 4n(4n + 1) = 1056 is possible when n = 8
4n (4n + 1) = 1088 not possible
4n(4n + 1) = 1120 not possible
4n(4n + 1) = 1332 possible when n = 9.
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