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:
( JEE mains 2024)
A. 9
B. 5
C. 7
D. 8
Ans:- (c)
4, 9, 14, 19, ...., up to 25th term
T₂5=4+(25-1)54+120=124
3, 6, 9, 12, up to 37th term
T37=3+(37-1)3=3+108= 111
Common difference of Ist series d₁ = 5
Common difference of IInd series d₂ = 3
First common term = 9, and their common difference = 15 (LCM of d, and d₂)
then common terms are 9, 24, 39, 54, 69, 84, 99
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