Question

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

Answer 1

Answer:

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

when there are 2 arithmetic progressions and you need to obtain a new sequence having terms common to both APs.

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

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)

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

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 4whereas for series 2 its 5

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 4whereas for series 2 its 5so the new AP will have c.d=lcm(4,5)=20

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 4whereas for series 2 its 5so the new AP will have c.d=lcm(4,5)=20the new series becomes

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 4whereas for series 2 its 5so the new AP will have c.d=lcm(4,5)=20the new series becomes 21,41,61,81....................401

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 4whereas for series 2 its 5so the new AP will have c.d=lcm(4,5)=20the new series becomes 21,41,61,81....................401401=21+(n-1)20

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 4whereas for series 2 its 5so the new AP will have c.d=lcm(4,5)=20the new series becomes 21,41,61,81....................401401=21+(n-1)20so n=20 terms is your answer