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8. Sequences and Series
hard
શ્રેણીઓ $4,9,14,19, \ldots . . .25$ માં પદ સુધી તથા $3,6,9,12, \ldots . . .37$ માં પદ સુધીના સામાન્ય પદોની સંખ્યા . . . . . .. છે.
A
$9$
B
$5$
C
$7$
D
$8$
(JEE MAIN-2024)
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
$\mathrm{T}_{37}=3+(37-1) 3=3+108=111$
Common difference of $\mathrm{I}^{\text {st }}$ series $\mathrm{d}_{\mathrm{l}}=5$
Common difference of $\mathrm{In}^{\text {nd }}$ series $\mathrm{d}_2=3$
First common term $=9$, and
their common difference $=15\left(\mathrm{LCM}\right.$ of $\mathrm{d}_1$ and $\mathrm{d}_2$ )
then common terms are
$9,24,39,54,69,84,99$
Standard 11
Mathematics
