Sequences And Series Question 5
Question 5 - 2024 (27 Jan Shift 1)
The number of common terms in the progressions $4,9,14,19, \ldots \ldots$, up to $25^{\text {th }}$ term and $3,6,9,12$, up to $37^{\text {th }}$ term is :
(1) 9
(2) 5
(3) 7
(4) 8
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Answer (3)
Solution
$4,9,14,19, \ldots$, up to $25^{\text {th }}$ term
$\mathrm{T}_{25}=4+(25-1) 5=4+120=124$
$3,6,9,12, \ldots$, up to $37^{\text {th }}$ term
$T_{37}=3+(37-1) 3=3+108=111$
Common difference of $\mathrm{I}^{\text {st }}$ series $\mathrm{d}_{1}=5$
Common difference of II ${ }^{\text {nd }}$ series $\mathrm{d}_{2}=3$
First common term $=9$, and
their common difference $=15\left(\mathrm{LCM}\right.$ of $\mathrm{d}{1}$ and $\left.\mathrm{d}{2}\right)$
then common terms are
$9,24,39,54,69,84,99$
