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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The common difference of the A.P.: $ a_1, a_2, \ldots, a_n $ is 13 more than the common difference of the A.P.: $ b_1, b_2, \ldots, b_n $. If $ b_1 = -277,; b_{33} = -385 $ and $ a_n = 327 $, then $ a_1 $ is equal to
Solution
Let common difference of A.P.'s are $ d_1 $ & $ d_2 $
$ d_1 = 13 + d_2 $
$ b_1 + 30d_2 = -277 \quad ...(1)$
$ b_1 + 42d_2 = -385 \quad ...(2)$
By (2) $-$ (1)
$ 12d_2 = -108 \Rightarrow d_2 = -9 $
$ \therefore d_1 = 4 $
Now $ a_n = 327 $
$ a_1 + 77d_1 = 327 $
$ a_1 + 308 = 327 $
$ a_1 = 19 $
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