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Question

Mark the correct alternative in the following question:

The 10th common term between the A.P.s 3, 7, 11, 15, ... and 1, 6, 11, 16, ... is

(a) 191 (b) 193 (c) 211 (d) none of these

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Solution

As, the common difference of the A.P. 3, 7, 11,15, ...=7-3=4 andthe common difference of the A.P. 1, 6, 11, 16, ...=6-1=5And, the common terms of both the A.P.s will be in A.P.So, the common difference of the A.P. of the common terms, d=LCM4, 5=4×5=20 andits first common term, a=11Now, the tenth common term, a10=a+10-1d=11+9×20=11+180=191

Hence, the correct alternative is option (a).

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