If (x-2) , 7 , (2x+1) are terms of an A.P , find x.

3 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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


hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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.

We’ve answered 318,917 questions. We can answer yours, too.

Ask a question