The number of common terms in the progressions 4,9,14,19,……, up to 25th term and 3,6,9,12,……, up to 37th term is :
Solutions · 1
Official 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 \[\mathrm{d}_1=5\]
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