SOLUTION: The three terms 7x+1, 9x+7, and 3x-4 (not necessarily in order) are 3 consecutive terms of an arithmetic sequence. Find the largest possible value of the common difference of such

Algebra.Com
Question 932628: The three terms 7x+1, 9x+7, and 3x-4 (not necessarily in order) are 3 consecutive terms of an arithmetic sequence. Find the largest possible value of the common difference of such an arithmetic sequence.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Try it all 6 possible ways to order them:

(1) 7x+1, 9x+7, 3x-4 

Common difference = (9x+7)-(7x+1) = (3x-4)-(9x+7)
                        9x+7-7x-1 = 3x-4-9x-7
                             2x+6 = -6x-11
                               8x = -17
                                x = -17/8 = -2.125
  
Common difference = 2x+6 = 2(-2.125)+6 = 1.75

(2) 7x+1, 3x-4, 9x+7

Common difference = (3x-4)-(7x+1) = (9x+7)-(3x-4)
                        3x-4-7x-1 = 9x+7-3x+4
                            -4x-5 = 6x+11
                             -10x = 16
                                x = 16/(-10) = -8/5 = -1.6
  
Common difference = -4x-5 = -4(-1.6)-5 = 1.4

(3) 9x+7, 7x+1, 3x-4

Common difference = (7x+1)-(9x+7) = (3x-4)-(7x+1)
                        7x+1-9x-7 = 3x-4-7x-1
                            -2x-6 = -4x-5
                               2x = 1
                                x = 1/2 = 0.5

Common difference = -2x-6 = -2(0.5)-6 = -7
  

(4) 9x+7, 3x-4, 7x+1

Common difference = (3x-4)-(9x+7) = (7x+1)-(3x-4)
                        3x-4-9x-7 = 7x+1-3x+4
                           -6x-11 = 4x+5
                             -10x = 16
                                x = 16/(-10) = -8/5 = -1.6
                                x = -8/5 = -1.6

Common difference = -6x-11 = -6(-1.6)-11 = -1.4

(5) 3x-4, 7x+1, 9x+7

Common difference = (7x+1)-(3x-4) = (9x+7)-(7x+1)
                        7x+1-3x+4 = 9x+7-7x-1
                             4x+5 = 2x+6
                               2x = 1
                                x = 1/2 = 0.5

Common difference = 4x+5 = 4(0.5)+5 = 7


(6) 3x-4, 9x+7, 7x+1

Common difference = (9x+7)-(3x-4) = (7x+1)-(9x+7)
                        9x+7-3x+4 = 7x+1-9x-7
                            6x+11 = -2x-6
                               8x = -17
                                x = -17/8 = -2.125

Common difference = 6x+11 = 6(-2.125)+11 = -1.75

Case 5 gives the largesr common difference of 7

Edwin
RELATED QUESTIONS

The terms 5 + x, 8, and 1 + 2x are consecutive terms in an arithmetic sequence. Determine (answered by MathLover1,josgarithmetic)
The first three terms of an arithmetic sequence, in order, are 2x + 4, 5x – 4, and 3x +... (answered by edjones,Edwin McCravy)
find what x is so that 3x-1, 5x-4 and 2x+8 are consecutive terms of an arithmetic... (answered by jim_thompson5910)
If (x+1), (-2x+4) and (x+15) are 3 consecutive terms of an arithmetic sequence, determine (answered by ikleyn)
3x-1/4 ;2x-1/3 ;7x-5/12 Prove that these are terms of an arithmetic... (answered by richwmiller)
1. Find the 25th term of the arithmetic sequence ‒7, ‒4, ‒1, 2, ... 2.... (answered by MathLover1,greenestamps)
2x-4;x+5 and 3x-1 are the first three terms of an arithmetic sequence.(I) show that x=5... (answered by ikleyn)
The sum of two consecutive terms in the arithmetic sequence 1, 4, 7, 10, ... is 299. Find (answered by scott8148)
The first two terms of an arithmetic sequence are 1/8 and 19/24 . What is the... (answered by ewatrrr)