The number of common terms in the progression | vedclass

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Question

$4,9,14,19, \ldots$, up to $25^{	ext {th }}$ term

$\mathrm{T}_{25}=4+(25-1) 5=4+120=124$

$3,6,9,12, \ldots$, up to $37^{	ext {th }}$ term

$

Vedclass · Accepted Answer

$7$

Vedclass · Answer

$4,9,14,19, \ldots$, up to $25^{	ext {th }}$ term

$\mathrm{T}_{25}=4+(25-1) 5=4+120=124$

$3,6,9,12, \ldots$, up to $37^{	ext {th }}$ term

$\mathrm{T}_{37}=3+(37-1) 3=3+108=111$

Common difference of $\mathrm{I}^{	ext {st }}$ series $\mathrm{d}_{\mathrm{l}}=5$

Common difference of $\mathrm{In}^{	ext {nd }}$ series $\mathrm{d}_2=3$

First common term $=9$, and

their common difference $=15\left(\mathrm{LCM}ight.$ of $\mathrm{d}_1$ and $\mathrm{d}_2$ )

then common terms are

$9,24,39,54,69,84,99$

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 :

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