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The number of terms which are common in the two series 17 , 21 , 25 , … , 417 and 16 , 21 , 26 , … , 466 is
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Nancy verma - Apr 17, 2023
Total no. of terms in the sequence1= 417-17/4 - 1 =101
Total no. of terms in the sequence 2 = 465-15/5 +1=91
Nth term of the first sequence = 4n+13
Mth term of the second sequence = 5m+11
4n+13=5m+11
5m-4n=2
possible integral values of n that satisfy 5m = 2+4n are (2,7,12,..,97)
the total no. of terms common in both the sequence is 20.
My answer is 20.
RaZeN - Apr 17, 2023
First term = 21, common difference = LCM(4,5) = 20
417 = 21 + (n-1)20
n = 20
Shanky Verma - Apr 17, 2023
20
Adit Agarwal - Apr 17, 2023
20
Ayushi verma - Apr 17, 2023
My answer is 20
As the common terms in both the series are 21, 41, 61, 81, ..........
a20 = a+(n-1)d = 21+(20-1)20
= 401 (last common term of both the series)
So, there are 20 numbe of terms which are common in both the series
Simran Raman - Apr 17, 2023
20, :- 20,41,61,81,101,121,141,161,181,201,221,241,261,281,301,321,341,361,381,401
Samarth Khurana - Apr 17, 2023
20