Question

The first term of two A.P.s are equal and the ratios of their common differences is 1:2 . if the 7th term of first A.P and 21st term of the second A.P are 23 and 125 respectively. find two A.P.S ​

Answer 1

Answer:

Let the first term of first A.P. be a and common diff. be d.

Let the the first term of second A.P. be a and common difference be 2d.

7th term =a+6d=23

a+40d=125 subtracting:-

34 d=102

d=102/34=3

a=5

first A.P.=5,8,11,14,17,20,23,......

second A.P=5,11,17,23,.....

Answer 2

Let AP1  be a,a+d,a+2d,......

AP2 be a,a+D,a+2D,.....

given,7th term of AP1=23.......eq 1

21st term of AP2=125........eq2

eq1-eq2

this implies,a+6d-a-20D

=6d-20D=23-125

=6d-20D=-102

=20d-6d=102

as ratio of common difference is 1:2,let d=d and D =2d

=20(2d)-6d=102

40d-6d=102

34d=102;17d=51

d=3

a7=a+6d=23

a+18=23;a=5

AP1=5,8,11,14,......

D=2d=6

AP2=5,11,17,.....

hope this helps u...