Q. 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 : (1) 9 (2) 5 (3) 7 (4) 8

Ans. (3)
Sol. 4,9,14,19,…, up to 25th term
T_25=4+(25-1)5=4+120=124
3,6,9,12,…, up to 37th term
T_37=3+(37-1)3=3+108=111
Common difference of 1st series d_1=5
Common difference of 2nd series d_2=3
First common term =9, and
their common difference =15( LCM of d_1 and d_2 )
then common terms are
9,24,39,54,69,84,99