MCQ
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 :
- A$9$
- B$5$
- ✓$7$
- D$8$
✓
Answer
Correct option: C.
$7$
c
$4,9,14,19, \ldots$, up to $25^{\text {th }}$ term
$4,9,14,19, \ldots$, 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
$9,24,39,54,69,84,99$
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