SOLUTION: S is an arithmetic series. S12 = 150 S25 = 875 What is the value of S40? Round to 2 decimal places.

Algebra ->  Sequences-and-series -> SOLUTION: S is an arithmetic series. S12 = 150 S25 = 875 What is the value of S40? Round to 2 decimal places.      Log On


   

Question 1161258: S is an arithmetic series.
S12 = 150
S25 = 875
What is the value of S40? Round to 2 decimal places.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

S is an arithmetic series.
so, nth term formula is:
S%5Bn%5D=S%5B1%5D%2Bd%28n-1%29
if S%5B12%5D+=+150, we have
150=S%5B1%5D%2Bd%2812-1%29
150=S%5B1%5D%2B11d.......solve for S%5B1%5D
S%5B1%5D=150-11d......eq.1

if S%5B25%5D+=+875, we have
875=S%5B1%5D%2Bd%2825-1%29
875=S%5B1%5D%2B24d.....solve for S%5B1%5D
S%5B1%5D=875-24d......eq.2
from eq.1 and eq.2 we have
150-11d=875-24d...solve for d
24d-11d=875-150
13d=725
d=725%2F13
go to
S%5B1%5D=150-11d......eq.1, substitute d
S%5B1%5D=150-11%28725%2F13%29
S%5B1%5D=150-7975%2F13
S%5B1%5D=-6025%2F13

your formula is:
S%5Bn%5D=-6025%2F13%2B%28725%2F13%29%28n-1%29

then, the value of S%5B40%5D is:
S%5B40%5D=-6025%2F13%2B%28725%2F13%29%2840-1%29
S%5B40%5D=-6025%2F13%2B%28725%2F13%29%2839%29
S%5B40%5D=-6025%2F13%2B2175
S%5B40%5D=22250%2F13
S%5B40%5D=1711.5384615384617....round to 2+decimal places
S%5B40%5D=1711.54


Answer by MathTherapy(10552) About Me  (Show Source):