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2,5,8,.........100 terms 3,5,7...........100 terms Find the sum of all the common terms of both the AP’s?

2,5,8,.........100 terms
3,5,7...........100 terms
 
Find the sum of all the common terms of both the AP’s?

Grade:

6 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
for 2,5,8,............100 terms
for 3,5,7.............100 terms
as we can seethat second serieshasallodd termstill3+(99)2=201
and 1stseries has last term as 2+(99)3=299
as we can see from aboveevery alternate termof 1stseries is present in 2ndalso.(as they are odd)
So the sum ofcommonterms of Ap’s=5+11+17+.......+201
=n/2(a+l)
=34/2(5+201)
=17(206)
=3502
Thanks and regards
Shaik Aasif
askIITians faculty
Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hello Student,
Common terms will come at interval of 6
=>
5,11,17 will go untill 201
Now apply the AP formulae
n/2*(2a+(n-1)*d)
Arun Kumar
Btech
IIT delhi
Askiitians Faculty
Student
8 Points
7 years ago
@arunkumar
Sir,
201 is not in the first ap then also should we consider this number.
 
Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hello Student,
You don’t have to take that term because its not in the first AP.
You have to take whatever biggest you get common untill 201.
Arun Kumar
Btech
IIT delhi
Askiitians Faculty
Student
8 Points
7 years ago
@arunkumar
Sir,
Is there any method of finding the greatest term in both the ap’s?
 
Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hello Student,
There is no other method than to find it by find the closest term to 201.
By followin formulae
2+3(n1-1)<=201 where n1 is integer.
3+2(n2-1)<=201 where n2 is integer.
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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