Question

number of common terms to the two sequence 17,21,25,.....417 and 16,21,26.....466 is

Answer 1

always remember
when there are 2 arithmetic progressions and you need to obtain a new sequence having terms common to both APs.
the common difference for the new sequence will be
lcm(c.d of AP 1,c.d of AP 2)
in this case c.d of series 1 is 4
whereas for series 2 its 5
so the new AP will have c.d=lcm(4,5)=20
the new series becomes
21,41,61,81....................401
401=21+(n-1)20
so n=20 terms is your answer
feel free to ask doubt
thank you

Answer 2

Answer:

The total number of terms common in both the sequences is 20.

Explanation:

Total number of terms in the sequence 17, 21, 25 …417 is 101

Total number of terms in the sequence 16, 21, 26 …466 is 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 number of terms common in both the sequences is 20.

Hope this helps!