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  4. Number of terms common in the first 100 terms of the arithmetic progression 1 + 4 + 7 + 10 + 13 + ...... and 2 + 6 + 10 + 14 + ........ is

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Q. Number of terms common in the first 100 terms of the arithmetic progression $1 + 4 + 7 + 10 + 13 + $ ...... and $2 + 6 + 10 + 14 +$ ........ is

Sequences and Series

Solution:

$T _{100}=1+(100-1) 3=1+297=298$
common terms are $10+22+34+\ldots \ldots . .+298$
common terms are $10+22+34+\ldots \ldots . .+298$
$298=10+(n-1) 12=12 n-2 $
$12 n=300 \Rightarrow n=25 \Rightarrow (C)$