IIT JEE , AIEEE Forum - Mathematics , Algebra

sinjan.j

Problem goes like this ?..
The first A.P ? 2,5,8,11,? up to 50 terms
The 2nd AP - 3,5,7,9,?.. upto 60 terms
Find the number of identical terms in between both The AP.

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I did my answer like dis..
I expanded both the AP?s to some extent and found out the first few identical terms and the last identical term.
Identical terms were like this - > 5,11,17,?.. 119
I found that the identical terms were in AP and their common difference was 6.
So I used the formula
A+(N-1)D = last term
5+(N-1)6 = 119
And I got N=20.

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Answer is correct.. but expanding and finding out the terms was pretty hectic and time consuming? any shortcut methods to solve this problem???

akhil_o

general term of AP1=2+3d
AP2=3+2d

so for all
nos of form 2+3k and 2k+3,
2+3k<=149
2k+3<=121
will be a prt

LCM is 6 of common difference
first term is 5
so simply
series=5+6r
now it should be easy to find N=20

bvsatyaram

Well done Akhil !!!
The whole crunch of the problem is to get the common series...

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