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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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