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
As, the common difference of the A.P. $3,7,11,15, \ldots=7-3=4$ and
the common difference of the A.P. $1,6,11,16, \ldots=6-1=5$
And, 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, $d=\operatorname{LCM}(4,5)=4 \times 5=20$ and
its first common term, $a=11$
Now, the tenth common term, $a_{10}=a+(10-1) d$
$=11+9 \times 20$
$=11+180$
$=191$
Hence, the correct alternative is option (a).
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