If (x-2) , 7 , (2x+1) are terms of an A.P , find x.
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calendarEducator since 2010
write12,554 answers
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The consecutive terms of an AP have a common difference.
So 2x + 1 - 7 = 7 - (x - 2)
=> 2x - 6 = 9 - x
=> 3x = 15
=> x = 15/3
=> x = 5
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calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Given that:
(x-2) , 7 , (2x+1) are terms of an arithmetical progression.
Then, we will assume that the common difference is r .
Then we know that:
7 = (x-2) + r
==> 7 - r = x-2
==> x = 9 - r ................(1)
Also, we know that:
2x+1 = 7 + r
==> 2x = 6 + r ..................(2)
Now we will add (1) and (2).
==> 3x = 15
==> x = 15/3 = 5
To check:
5 -2 = 3
2x +1 = 2(5) + 1 = 11
==> 3, 7, 11 are terms of an A.P where the common difference is r = 4
==> x = 5
To find x , if (x-2) , 7 , (2x+1) are terms of an A.P.
Solution:
If x-2, 7 and 2x+1 are the successive terms of an arithmetic progression, then the the difference between the successive terms must be same:
=> 7- (x-2) = 2x+1-7.
7-x+2 = 2x-6.
9-x = 2x-6.
9+6 = 2x+x.
15 = 3x.
15/3 = 3x/3.
5 = x.
So x = 5.
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