SOLUTION: What is the sum of 75 terms when the sequence is 5, 12, 29, 41

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
RELATED QUESTIONS
The 11th term of an arthmetric sequence is 57 and the sum of the first and fourth terms... (answered by hovuquocan1997)

The 11th term of an arithmetic sequence is 57 and the sum of the first and fourth terms... (answered by MathTherapy)

Find the sum of the geometric sequence �3, 15, �75, 375, � when there are 7 terms (answered by stanbon)

What is the sum of the arithmetic sequence 5, 11, 17 �, if there are 24... (answered by math-vortex)

The sum of a geometric sequence 2 - 6 + 18 - 54 + ... - tn is - 29 524. Find the... (answered by ikleyn)

Find the sum of the first 12 terms of the arithmetic sequence whos general term is an=3n+ (answered by dkppathak)

We have a sequence: 11, 17, 2, 29, 31, 41, 47, ... What is the eighth number? And... (answered by ikleyn)