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The number of common terms in the two sequences 17, 21, 25,…..417 and 16, 21 26,.....466 is

1. 78
2. 19
3. 20
4. 27
5. 22
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+1 vote

Alternate method :

difference of first series = 4, difference of second series =5

so difference of common series will be always  LCM (4,5 )= 20 .

by seeing both series ...we can easly find first term = 21,

and last term of common series will be less than or equal to 417 ,bcoz common series will go up to common of both and first sequence is till 417 .

series like 21 ,41,61.... 401....(bcoz 401%20=1 ,)

so 401= 21+ (n-1)20

380/20= (n-1)

n= 20 hence answe is 3)

answered by (2.2k points)
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+1 vote
No of terms in first sequence be n

417=17+(n-1)4

n=101

No of terms in second seq be m

466=16+(m-1)5

m=91

First common term is 21 next is 41

Common difference=20

Now last common term will be less than or equal to 417 and not 466

Last term in common seq will be 401

401=21+(k-1)20

380/20=k-1

k=20
answered by (1.6k points)