the first term of two APs are equal and the ratios of their common difference is 1:2.if the 7th term of the first AP and 21st term of second AP are 23 and 125.find two APs?
Answers
AnswEr :
⋆ Let the First Term of Both APs be a.
⋆ Common Difference of First AP be d and, of Second AP be 2d.
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QUESTION:-
the first term of two APs are equal and the ratios of their common difference is 1:2.if the 7th term of the first AP and 21st term of second AP are 23 and 125.find two APs?.
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ANSWER
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• SOLVE FOR THE FIRST A.P
First term = a
Common difference = d
a7 = 23
a + 6d = 23
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SOLVE FOR THE SECOND A.P
First term = a ( given)
common difference = b
a21 = 125
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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,
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let,
•d= 1x { For x is some common positive integer}
•b = 2x { for x is some common positive integer}
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•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,
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•Replacing the value of d in equation 1
we get,
a + 6d = 23
a = 23 - 6(3)
a = 23 - 18
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HENCE.
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THE FIRST A.P
THE SECOND A.P