Question

In the arithmetic progressions 2,5,8, .. upto 50 terms, and 3,5,7,9, ... upto 60 terms, find how many terms are identical.

Answer 1

For the first A.P

$A_n=2+(x-1)3=3x-1$ when $0<x<51$

For second A.P,

$B_n=3+(y-1{)}^2=2y+1$ when $0<y<61$

where x and y are inyegers.

when x is an even no., it satisfies this condition.

Hence

x=2, y=2

x=4, y=5

x=6, y=8

.

.

.

.

.

x=40, y=59

Hence, 20 terms are identical.