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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 - Mathematics

MCQ

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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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Q 22 | Page 52
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