Verified Solution • 2025–26 Session moderate

QJEEM24Ma095f: JEE Main 2024 Mathematics - Class 11 JEEM24Ma095f Solution: The number of common terms in the progressions , up to term and …

The number of common terms in the progressions

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

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

Multiple Choice Options

  • A 9
  • B 8
  • C 5
  • D 7

Step-by-Step Verified Solution

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

T25=4+(25−1)5=4+120=124\mathrm{T}_{25}=4+(25-1) 5=4+120=124

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

T37=3+(37−1)3=3+108=111\mathrm{T}_{37}=3+(37-1) 3=3+108=111

Common difference of Ist \mathrm{I}^{\text {st }} series d1=5\mathrm{d}_1=5

Common difference of IInd \mathrm{II}^{\text {nd }} series d2=3\mathrm{d}_2=3

First common term =9=9 , and their common difference =15(LCM⁡=15\left(\operatorname{LCM}\right. of d1\mathrm{d}_1 and d2)\left.\mathrm{d}_2\right) then common terms are 9,24,39,54,69,84,999,24,39,54,69,84,99

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