Answer :
The first AP is: 5,8,11,14,… and the second AP is: 5,11,17,23,…
Let the first term be a. Common differences of the first and second APs be d1 and d2 respectively.
We are given that the ratio of d1 to d2 is 1:2, so d2 =2d1 .
We are also given that the 7th term of the first AP is 23 and the 21st term of the second AP is 125.
These can be expressed in the following equations:
a+6d1=23
a+20d2 =125
Substituting d2 =2d1 into the second equation, we get:
a+20⋅2d1=125
a+40d1 =125
Now we have two independent equations with two unknowns. Solving for a and d1 , we get:
a=5
d1 =3
Therefore, the first AP is: 5,8,11,14,… and the second AP is: 5,11,17,23,…
Question
The first term of two A.P.s are equal and the ratios of their common difference is 1:2 .if the 7th term of the first A.P and 21st term of the second A.P are 23 and 125 respectively .Find the two A.P.s
