Question

the first term of two APs are equal and the ratio of their common difference is 1 is to 2 if the 7th term of first A. P and 21th term of second AP are 23 and 125 respectively find two APs​

Answer 1

The for the question is given above

Answer 2

The first AP  is 5,8,11..

The second AP is 5,11,17..

Step-by-step explanation:

let the first term be a

common difference be d

a7 = 23

a+6d = 23

a= 23-6d ..(1)

for the second AP

let common difference be y

a21 = 125

a+20y = 125 ..(2)

putting the value of a from 1 in 2

a+20y = 125

23-6d+20y=125

20y-6d=102

10y - 3d =51..(3)

ratio given

$\frac{d}{y}= \frac{1}{2} \\\\d= 1x \\\\y = 2x$

place the vale in equation 3 we get

10y-3d=51

10(2x) -3(x) = 51

20x-3x=51

17x=51

x = $\frac{51}{17}$

x = 3

hence , d= 3

and y = 2(3) = 6

now ,

a+6d =23

putting the value of d we get

a=5

therefore , The first AP  is 5,8,11..

The second AP is 5,11,17..

#Learn more:

The first term of an (AP) is-8.the ratio of the 7th term to the 9th term is 5:8 calculate the common difference of the progression​

https://brainly.com/question/14626215