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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

##### 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.

##### RaZeN - Apr 17, 2023

First term = 21, common difference = LCM(4,5) = 20

417 = 21 + (n-1)20

n = 20

20

20

##### Ayushi verma - Apr 17, 2023

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

20