SOLUTION: Find the number of terms and the values of the arithmetic means that should be inserted between 1 and 50 in order to make the sum of the seris equal 459.

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Question 878349: Find the number of terms and the values of the arithmetic means that should be inserted between 1 and 50 in order to make the sum of the seris equal 459.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
S = ½(a + an)n
459 = ½(1 + 50)n
918=51n
18=n
S = ½(2a + (n-1)d)n
459 = ½(2 + (17)d)18
459=9*(2+17d)
459/9=2+17d
49=17d
49/17=d
1+49/17=66/17 is the second term
add 66/17 to the last term
There are 18 terms altogether including 1 and 50
1 1
2 3.88235294
3 6.76470588
4 9.64705882
5 12.5294118
6 15.4117647
7 18.2941176
8 21.1764706
9 24.0588235
10 26.9411765
11 29.8235294
12 32.7058824
13 35.5882353
14 38.4705882
15 41.3529412
16 44.2352941
17 47.1176471
18 50