Question

Find the no. of common terms in both Arithmetic progression $3,7,11,....$ (upto 50 terms) and $5,8,11,....$(upto 60 terms)

Answer 1

b'$3,7,11,15,19,23,27,.........50$ terms

$5,8,11,14,17,20,23,........60$ terms

$therefore$

sequence of common terms is an $AP\Rightarrow$

$11,23,..........n$ terms

Last terms of $1^{st}$ seq = $3+49\times 4=199$

Last terms of $2^{nd}$ seq $5+59\times 3=182$

$\therefore$

$11+(n-1)12le182$

$12(n-1)le171$

$nle15.25$ $n=15$

$\therefore$ Number of common terms $=15$

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