The number of common terms in the progressions 4,9,14,19,, up to 25^{{th}{~}} term and 3,6,9,12, . . . ., up to 37^{{th}{~}} term is :: Sequence & Series (Mathematics)

(b): $4,9,14,19,\ldots$ are in A.P. with $d_{1} = 5,n_{1} = 25\\$ $3,6,9,12,\ldots$ are in A.P. with $d_{2} = 3,n_{2} = 37\\$ L.C.M. $\left( d_{1},d_{2} \right) = 15\\$ Common terms $= 9,24,39,54,69,84,99$