SOLUTION: The first three terms of an arithmetic sequence, in order, are 2x + 4, 5x – 4, and 3x + 4. What is the sum of the first ten terms of the sequence?

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Question 257426: The first three terms of an arithmetic sequence, in order, are 2x + 4, 5x – 4, and
3x + 4. What is the sum of the first ten terms of the sequence?
Found 2 solutions by edjones, Edwin McCravy:
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
3x+4-(2x+4)=x subtract the 1st term from the 3rd term
The difference between the 2nd and 1st term must be half of x or .5x
2x+4+ .5x =5x-4
2.5x=8
x=3.2
d=.5*3.2=1.6 difference between each number.
Now we can find the 10th term.


=24.8
formula for the sum of a finite arithmetic sequence.

=176
.
Ed
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
The first three terms of an arithmetic sequence, in order, are 2x + 4, 5x – 4, and
3x + 4. What is the sum of the first ten terms of the sequence? 

If it's an arithmetic sequence then

the second term minus the first term must be equal to third term minus the second term.

So 

(5x-4) - (2x+4) = (3x+4) - (5x-4)

5x - 4 - 2x - 4 = 3x + 4 - 5x + 4
 
         3x - 8 = -2x + 8
    
        3x + 2x = 8 + 8

             5x = 16

              x = 

     
2x + 4, 5x – 4, and 3x + 4

Substitute  for x in all three terms:

 

 














So the common difference d is 





the sum of the first n terms is given by the formula

 and  and 











Edwin
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