SOLUTION: six numbers form an arithmetic sequence. The mean of the numbers equals the range. If the smallest number is 30, what is the largest number?

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Question 264322: six numbers form an arithmetic sequence. The mean of the numbers equals the range. If the smallest number is 30, what is the largest number?
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
If the smallest number is 30, what is the largest number?
Guess and check method:
Attempt 1 adding 30
30 60 90 120 150 180 range is 180-30=150 mean is 630/6=105 nope
Attempt 2 adding 10
30 40 50 60 70 80 range is 80-30=50 mean is 330/6=55 nope
Attempt 3 adding 5
30 35 40 45 50 55 range is 55-30=25 mean is 255/6=42.5 nope
Attempt 4 adding 15
30 45 60 75 90 105 range is 105-30=75 mean is 405/6=67.5 nope
Attempt 5 adding 9
30 39 48 57 66 75 range is 75-30=45 mean is 315/6=52.5 nope
Attempt 6 adding 11
30 41 52 63 74 85 range is 85-30=55 mean is 330/6=57.5 nope
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Attempt 7 adding 12
30 42 54 66 78 90 range is 90-30=60 mean is 360/6=60 BINGO
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Formula method
(30+(30+n)+(30+2n)+(30+3n)+(30+4n)+(30+5n))/6=x
(30+5n)-30=x
Simplify both equations and solve for "n"
(30+(30+n)+(30+2n)+(30+3n)+(30+4n)+(30+5n))/6=x
(180+15n)/6=x
30+(5n/2)=x
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(30+5n)-30=x
5n=x
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30+(5n/2)=5n
60+5n=10n
60=5n
12=n
Last number in sequence is (30+5n) replace n with 12
30+5(12)
30+60
90 is the largest number in the sequence