Question

tow different aps have the common difference the first term of tha first AP is equal to the more than thirce of the second aps first term if seventh AP is 29 then find the two different ap​

Answer 1

Answer:FIRST A.P = 5,8,11......

SECOND A.P = 5,11,17.....

Step-by-step explanation:

FOR THE FIRST A.P

First term = a

Common difference = d

a7 = 23

a + 6d = 23

a = 23 - 6d ----------------- 1

FOR THE SECOND A.P

First term = a ( given)

common difference = b

a21 = 125

a + 20b = 125 -------------- 2

Replacing the value of a from equation 1 to equation 2.

we get,

a + 20b = 125

23 - 6d + 20b = 125

20b - 6d = 125 - 23

20b - 6d = 102

2(10b - 3d) = 102

10b - 3d = 51 ------------ 3

Given,

d/b = 1/2

let,

d= 1x { For x is some common positive integer}

b = 2x { for x is some common positive integer}

Replacing the value of d and b in equation 3

we get,

10b - 3d = 51

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

20x - 3x = 51

17x = 51

x = 3

Therefore,

d = 3

b = 6

Replacing the value of d in equation 1

we get,

a + 6d = 23

a = 23 - 6(3)

a = 23 - 18

a = 5

THE FIRST A.P

5,8,11.........

THE SECOND A.P

5,11,17...........

Step-by-step explanation:

Hope it helped u