SOLUTION: Find the 45th partial sum of the geometric sequence 8+12+18+27+....

Algebra ->  Sequences-and-series -> SOLUTION: Find the 45th partial sum of the geometric sequence 8+12+18+27+....      Log On


   



Question 880060: Find the 45th partial sum of the geometric sequence
8+12+18+27+....

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
To find r we divide matrix%281%2C2%2C2nd%2Cterm%29%2Fmatrix%281%2C2%2C1st%2Cterm%29%22%22=%22%2212%2F8%22%22=%22%223%2F2

As a check, also divide matrix%281%2C2%2C3rd%2Cterm%29%2Fmatrix%281%2C2%2C2nd%2Cterm%29%22%22=%22%2218%2F12%22%22=%22%223%2F2

and

matrix%281%2C2%2C4th%2Cterm%29%2Fmatrix%281%2C2%2C3rd%2Cterm%29%22%22=%22%2227%2F18%22%22=%22%223%2F2

So r%22%22=%22%223%2F2

Formula for the sum of the first n terms of a geometric series:

S%5Bn%5D%22%22=%22%22%28a%5B1%5D%28r%5En-1%29%29%2F%28r-1%29

where n%22%22=%22%2245 and r%22%22=%22%223%2F2, a%5B1%5D%22%22=%22%228

S%5B45%5D%22%22=%22%22%288%28%283%2F2%29%5E45-1%29%29%2F%28%283%2F2%29-1%29%22%22=%22%221343465861

Edwin