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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
If the sum of the first four terms of an A.P. is $6$ and the sum of its first six terms is $4$, then the sum of its first twelve terms is
Solution
$\frac{4}{2}(2a + 3d) = 6 \Rightarrow 2a + 3d = 3 \quad ...(1)$
Sum of first $6$ terms $S_6 = 4$
$\frac{6}{2}(2a + 5d) = 4 \Rightarrow 2a + 5d = \frac{4}{3} \quad ...(2)$
(2) – (1)
$(2a + 5d) - (2a + 3d) = \frac{4}{3} - 3$
$\Rightarrow 2d = -\frac{5}{3} \Rightarrow d = -\frac{5}{6}$
$2a + 3\left(-\frac{5}{6}\right) = 3 \Rightarrow 2a = \frac{11}{2} \Rightarrow a = \frac{11}{4}$
$S_{12} = \frac{12}{2}\left(2a + 11d\right)$
$= 6\left(\frac{11}{2} + 11\left(-\frac{5}{6}\right)\right)$
$= 6\left(\frac{33 - 55}{6}\right) = -22$
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