Determine whether the series is geometric. Justify your answer.
4+20+100+500+...Determine whether the series is geometric. Justify your answer.
-150+15-1.5+0.15-...Determine whether the series is geometric. Justify your answer.
3-9+18-54+...Determine whether the series is geometric. Justify your answer.
256-64+16-4+...For the geometric series, determine the values of a and r. Then, determine the indicated sum.
S_8 for 2+6+18+...
For the geometric series, determine the values of a and r. Then, determine the indicated sum.
S_{10} for 24-12+6-...
For the geometric series, determine the values of a and r. Then, determine the indicated sum.
S_{15} for 0.3 +0.003+0.00003...
For the geometric series, determine the values of a and r. Then, determine the indicated sum.
S_{12} for 1-\frac{1}{3}+\frac{1}{9}-...
For the geometric series, determine the values of a and r. Then, determine the indicated sum.
S_9 for 2.1-4.2+8.4-...
For the geometric series, determine the values of a and r. Then, determine the indicated sum.
S_{40} for 8-8+8-...
Determine S_n for each geometric series.
a=6, r=2, n=9
Determine S_n for each geometric series.
f(1)=2, r=-2, n=12
Determine S_n for each geometric series.
f(1)=729, r=-3, n=15
Determine S_n for each geometric series.
f(1)=2700, r=10, n=8
Determine S_n for each geometric series.
a=\frac{1}{2}, r=4, n=8
Determine S_n for each geometric series.
a=243, r=\frac{1}{3}, n=10
Determine the sum of each geometric series.
27+9+3+...+\frac{1}{243}
Determine the sum of each geometric series.
75+3.5+1.75+...+0.10937
Determine the sum of each geometric series.
1200+120+12+...+0.0012
Determine the sum of each geometric series.
\displaystyle \frac{1}{3}+\frac{2}{9}+\frac{4}{27}+\frac{8}{81}+...+ \frac{128}{6551}
Determine the sum of the geometric series.
5-15+45-...+3645
Determine the sum of the geometric series.
6-12+24-48+...-768
Determine the sum of the geometric series.
96 000-48 000+24 000-...+375
Determine the sum of the geometric series.
1-\frac{2}{3}+\frac{4}{9}-...+\frac{64}{729}
Determine the specified sum for the geometric series.
S_{10} for \sqrt{3}-3+3\sqrt{3}+...
Determine the specified sum for the geometric series.
S_{12} for \sqrt{2}x+2x+2\sqrt{2}x+...
Determine the specified sum for the geometric series.
S_{15} for 3+3x+3x^2...
Determine the sum of the geometric series.
10+5+\frac{5}{2}+...+\frac{5}{64}
Determine the sum of the geometric series.
1+x+x^2+x^3+...+x^k
The sum of 4+12+36+108+...+t_n is 4372. How many terms are in this series?
The third term of a geometric series is 24 and the fourth term is 36. Determine the sum of the first 10 terms.
In a lottery, the first ticket drawn wins a prize of $25. Each ticket drawn after that receives a prize that is twice the value of the preceding prize.
(a) Write a function to model the total amount of prize money given away.
In a lottery, the first ticket drawn wins a prize of $25. Each ticket drawn after that receives a prize that is twice the value of the preceding prize.
(b) Graph the function to determine how many prizes can be given out if the total amount of prize money is $2 million.
A bouncy ball bounces to \frac{2}{3} of its height when dropped on a hard surface. Suppose the ball is dropped from 20 m.
(a) What height will the ball bounce back up to after the sixth bounce?
A bouncy ball bounces to \frac{2}{3} of its height when dropped on a hard surface. Suppose the ball is dropped from 20 m.
(b) What is the total distance travelled by the ball after 10 bounces?
The air in the hot-air balloon cools as the balloon rises. If the air is not reheated, the balloon's rate of ascent will decrease.
The air in the hot-air balloon cools as the balloon rises. If the air is not reheated, the balloon's rate of ascent will decrease.
The air in the hot-air balloon cools as the balloon rises. If the air is not reheated, the balloon's rate of ascent will decrease.
Use the function \displaystyle
f(b) = 160(1-0.75^n)
to determine the height of the balloon after 10 min.
Three numbers, a, b, and c, form a geometric series so that a+b+c=35 and abc=1000. Determine the values of a, b, and c.
For a geometric series \frac{S_4}{S_8}=\frac{1}{17}. Determine the first three terms of the series if the first term is 3.
The sum of the first five terms of a geometric series is 186 and the sum of the first six terms is 378. If the fourth term is 48, determine a, r, t_{10}, and S_{10}.
Determine n if 3+3^2+3^3+..+3^n=9840.
If 2b-2, 2b+2 and 5b+1 are the first three terms of a geometric sequence, determine the sum of the first five terms.
1 Introduction to Geometric Series with an example
\displaystyle
\begin{array}{lll}
&S_n = \frac{a(r^n - 1)}{r -1}, \text{ if } &|r| >1 \\
&S_n = \frac{a(1- r^n )}{1 - r}, \text{ if } &|r| <1
\end{array}
2 Geometric Series without using the Formula
3 Geometric Series Formula
4 Geometric Series ex1
5 Geometric Series ex2
6 Geometric Series ex3
7 Infinite repeating decimals as Geometric Series
\displaystyle
\begin{array}{lll}
&S_{\infty} = \frac{a}{1 - r}, \text{ if } &|n| <1
\end{array}