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?

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) (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

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