Arithmetic Sequence
- Thread starter JustYourAverageFriend
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Steven G
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Let a = 1st term.
(a)+(a+d)+(a+2d)+ ... +(a+9d) = (a+19d) + (a+20d) + (a+21d)
10a+45d = 3a+60d
7a = 15d
0<a<20 implies a=15. So d=7
Now (15) + (15 + 1*7) + (15 + 2*7) + ... (15 + (n-1)*7) = 960
15n + 7*(n-1)*n/2 = 960
30n + 7n^2 - 7n = 1920
7n^2 + 23n - 1920 = 0
n=15
(a)+(a+d)+(a+2d)+ ... +(a+9d) = (a+19d) + (a+20d) + (a+21d)
10a+45d = 3a+60d
7a = 15d
0<a<20 implies a=15. So d=7
Now (15) + (15 + 1*7) + (15 + 2*7) + ... (15 + (n-1)*7) = 960
15n + 7*(n-1)*n/2 = 960
30n + 7n^2 - 7n = 1920
7n^2 + 23n - 1920 = 0
n=15