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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
Options
191
193
211
none of these
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Solution
\[\text { As, the common difference of the A . P . 3, 7, 11, 15, . . . = 7 - 3 = 4 and }\]
\[\text { the common difference of the A . P . } 1, 6, 11, 16, . . . = 6 - 1 = 5\]
\[\text { And, the common terms of both the A . P . s will be in A . P } . \]
\[\text { So, the common difference of the A . P . of the common terms, d = LCM }\left( 4, 5 \right) = 4 \times 5 = 20 \text { and }\]
\[\text { its first common term, } a = 11\]
\[\text { Now, the tenth common term, } a_{10} = a + \left( 10 - 1 \right)d\]
\[ = 11 + 9 \times 20\]
\[ = 11 + 180\]
\[ = 191\]
Hence, the correct alternative is option (a).
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