Question 127843: find the value of y in Y+8, 4y+6, 3y to make this an arithmetic sequence
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! If this is an arithmetic sequence, the same number must be added as you go from one to the next. So the number between y+4 and 4y+6 is the same as the number between 4y+6 and 3y. If you had the sequence 3, 5, 7, you would subtract 5-3 and get 2, and subtract 7-5 and get 2. Since they have the same difference, the sequence is arithmetic. So here, too, we need the same difference.
So (4y+6)-(y+8)=(3y)-(4y+6)
4y+6-y-8=3y-4y-6
3y-2=-y-6
4y=-4
y=-1
You can check that this y makes it an arithmetic sequence:
y+8, 4y+6, 3y becomes -1+8, 4(-1)+6, 3(-1) = 7, 2, -3, so -5 is being added each time.
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