Question 873472: What is the sum of 75 terms when the sequence is 5, 12, 29, 41
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 5, 12, 29, 41
an^3+bn^2+c*n+d=5
a+b+c+d=5
A*2^3+B*2^2+2C+D=12
8a+4b+2c+d=12
A*3^3+B*3^2+3C+D=29
27a+9b+3c+d=29
A*4^3+B*4^2+4C+D=41
64a+16b4c+d=41
a+b+c+d=5,
8a+4b+2c+d=12,
27a+9b+3c+d=29,
64a+16b+4c+d=41
a = -5/2, b = 20, c = -71/2, d = 23
-(5/2)*n^3+20*n^2-(71/2)*n+23=s
when n=1 s=5
when n=2 s=12
when n=3 s=29
when n=4 s=41
5, 12, 29, 41
here are the first 75 terms
5,12,29,41,33,-10,-103,-261,-499,-832,-1275,-1843,-2551,-3414,-4447,-5665,-7083,-8716,-10579,-12687,-15055,-17698,-20631,-23869,-27427,-31320,-35563,-40171,-45159,-50542,-56335,-62553,-69211,-76324,-83907,-91975,-100543,-109626,-119239,-129397,-140115,-151408,-163291,-175779,-188887,-202630,-217023,-232081,-247819,-264252,-281395,-299263,-317871,-337234,-357367,-378285,-400003,-422536,-445899,-470107,-495175,-521118,-547951,-575689,-604347,-633940,-664483,-695991,-728479,-761962,-796455,-831973,-868531,-906144,-944827
total of 75 terms
-17536700
or
a=-25/6
b=35
c= -473/6
d= 63
15,12,29,41,23,-50.0,-203,-461.0,-849,-1392.0,-2115.0,-3043.0,-4201.0,-5614,-7307.0,-9305.0,-11633.0,-14316,-17379,-20847.0,-24745,-29098.0,-33931,-39269.0,-45137.0,-51560.0,-58563,-66171,-74409.0,-83302.0,-92875,-103153.0,-114161,-125924.0,-138467,-151815,-165993.0,-181026,-196939.0,-213757.0,-231505.0,-250208,-269891,-290579.0,-312297,-335070,-358923.0,-383881.0,-409969,-437212.0,-465635,-495263.0,-526121,-558234,-591627.0,-626325,-662353,-699736.0,-738499,-778667.0,-820265.0,-863318,-907851.0,-953889.0,-1001457.0,-1050580,-1101283,-1153591.0,-1207529,-1263122,-1320395.0,-1379373,-1440081,-1502544.0,-1566787.0,
total =-29042950
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