Free Printable CHAPTER 6 DM015 (SUBTOPIC 6.2)

1.

Evaluate the geometric series described.
$3+15+75+375...,\ \ \ \ n=6$

a)

11,718

b)

10,603

c)

9,769

d)

$-\frac{3}{4}$

2.

Evaluate the geometric series $1-2+4-8,\ ...,\ \ \ \ \ \ \ n=8$

a)

$\frac{1}{3}$

b)

-86

c)

-87

d)

-85

3.

$a_1=-2,\ \ \ r=-2,\ \ \ S_n=22$ Determine the number of terms n in the series

a)

6

b)

7

c)

8

d)

5

4.

$1,\ -2,\ 4,\ -8,\ ...\ \ Find\ a_{11}$

a)

$-512$

b)

$-1024$

c)

$1024$

d)

$512$

5.

$2,\ 10,\ 50,\ 250,\ ...$ Find the explicit formula

a)

$a_n=10\cdot4^{\left(n-1\right)}$

b)

$a_n=2\cdot5^{\left(n-1\right)}$

c)

$a_n=10\cdot5^{\left(n-1\right)}$

d)

$a_n=5\cdot2^{\left(n-1\right)}$

6.

Write the repeating decimal as a fraction in simplest form.

0.222

a)

$\frac{11}{50}$

b)

$\frac{22}{100}$

c)

$\frac{2}{9}$

d)

$\frac{12}{31}$

7.

Write the repeating decimal as a fraction in simplest form.

32.323232...

a)

$32\ \frac{32}{100}$

b)

$32\ \frac{32}{99}$

c)

$32\ \frac{3}{8}$

d)

$32\ \frac{3}{11}$

8.

The sum of an infinite Geometric series is given by:

a)

$S=\frac{r}{1-a}$

b)

$S_n=\frac{a\ \left(1-r^n\right)}{1-r}$

c)

$S_n=\frac{a}{1-r^n}$

d)

$S=\frac{a}{1-r}$

9.

The first term of a geometric sequence is 5 and the sixth term is 160.What is the common ratio

a)

1

b)

2

c)

3

d)

4

10.

the 12th term of a geometric sequence is 2 and the 15th term is 54. Find the value of common ratio.

a)

1

b)

2

c)

3

d)

4

11.

Find S₂₀ for the geometric series with

a₁ = 1000 and r = 0.5.

a)

$1000\left(\frac{1}{2}\right)^{20}$

b)

$1000\left(1-\left(\frac{1}{2}\right)^{20}\right)$

c)

$2000\left(1-\left(\frac{1}{2}\right)^{20}\right)$

d)

$2000\left(\frac{1}{2}\right)^{20}$

CHAPTER 6 DM015 (SUBTOPIC 6.2)

Total questions: 11

Worksheet time: 6mins

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