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Answers
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...........
Answer:
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