"The number of common terms in the progressions $4,9,14,19, \ldots \ldots$, up to $25^{\text {th }}$ term and $3,6,9,12, \ldots \ldots$, up to $37^{\text {th }}$ term is :"

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Accepted Answer

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$4,9,14,19, \ldots$, 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

$\mathrm{T}_{37}=3+(37-1) 3=3+108=111$

Common difference of $\mathrm{I}^{\text {st }}$ series $\mathrm{d}_1=5$

Common difference of $\mathrm{II}^{\text {nd }}$ series $\mathrm{d}_2=3$

First common term $=9$, and their common difference $=15\left(\operatorname{LCM}\right.$ of $\mathrm{d}_1$ and $\left.\mathrm{d}_2\right)$ then common terms are $9,24,39,54,69,84,99$

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The number of common terms in the progressions

$4,9,14,19, \ldots \ldots$, up to $25^{\text {th }}$ term and

$3,6,9,12, \ldots \ldots$, up to $37^{\text {th }}$ term is :

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The number of common terms in the progressions $4,9,14,19, \ldots \ldots$, up to $25^{\text {th }}$ term and $3,6,9,12, \ldots \ldots$, up to $37^{\text {th }}$ term is :

Solution

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The number of common terms in the progressions

$4,9,14,19, \ldots \ldots$, up to $25^{\text {th }}$ term and

$3,6,9,12, \ldots \ldots$, up to $37^{\text {th }}$ term is :