Question

Find the number of common terms to the sequences 2, 4, 6, ...... 100 and 3, 6, 9, ...... 99

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Answer 1

First term = 6
The sequence of common terms will be
6, 12, 18 ...... 96
One important thing to note here is that the common terms from A.P
with common difference d, which is the L.C.M of the common difference of the given A.Ps
a=6
d=6
$t_n$=96
$\Rightarrow$a+(n-1)d=96
6+(n-1)6=96
6+(n-1)=90
n-1=15
n=16