Question 26074: 1) Use the geometric series of numbers 1, 2, 4, 8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
b) Using the formula for the nth term of a geometric series, what is the 24th term?
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
pls help
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! ) Use the geometric series of numbers 1, 2, 4, 8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
b) Using the formula for the nth term of a geometric series, what is the 24th term?
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms? SUM IS GIVEN BY
SN=A(R^N-1)/(R-1)
S10=1*(2^10-1)/(2-1)=2^10-1
SEE THE FOLLOWING EXAMPLE AND SOLVE
Use the geometric series of numbers 1, 1/2, 1/4, 1/8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
R=(1/2)/1=1/2...IT IS SAME FOR ANY 2 CONSECUTIVE TERMS...SAY
(1/8)/(1/4)=1/2...ETC......
b) Using the formula for the nth term of a geometric series, what is 10th term?
TN=A*(R)^(N-1)=1*(1/2)^(N-1)
T10=(1/2)^(10-1)=(1/2)^9
c) Using the formula for the nth term of a geometric series, what is 12th term?
T12=(1/2)^11
d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
THE NUMBERS TEND TO ZERO AS N INCREASES TO LARGE NUMBERS AND TOWARDS INFINITY.
SUM OF A G.P. TO INFINITE TERMS WITH R<1 IS GIVEN BY
A/(1-R)=1/(1-0.5)=2
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