Free Printable Sequences, Series, Binomial Thm Review

1.

Find the sum of the infinite geometric sequence.

2 + 0.4 + 0.08 ...

a)

s = 2.5

b)

s = 6.5

c)

s = 0.1

d)

s = 4.5

e)

s = 0.5

2.

Find the sum of the infinite geometric series.
$\sum_{n=0}^{\infty}7\left(\frac{1}{3}\right)^n$

a)

$\frac{2}{21}$

b)

$\frac{2}{7}$

c)

$-\frac{1}{3}$

d)

$\frac{21}{2}$

e)

undefined

3.

Find the sum of the indicated terms of the geometric sequence. $\sum_{n=1}^83\left(4\right)^{n-1}$

a)

s = 65,535

b)

s = 65,538

c)

s = 65,532

d)

s = 65,541

e)

s = 262,140

4.

Find the sum of the indicated terms of the geometric sequence.

6, 18, 54 ... (to 8 terms)

a)

s = 19,686

b)

s = 19,692

c)

s = 19,680

d)

s = 19,674

e)

none of the above

5.

Find the eighth term of the geometric sequence whose second and fourth terms are 6 and 54.

a)

a₈ = 39,366

b)

a₈ = 4,374

c)

a₈ = 13,122

d)

a₈ = 1,458

e)

a₈ = 486

6.

Use summation notation to write the sum. $-3-6-12-....-48$

a)

$\sum_{n=1}^5-3\left(2\right)^{n-1}$

b)

$\sum_{n=1}^4-3\left(2\right)^{n+1}$

c)

$\sum_{n=0}^4-3\left(2\right)^{n-1}$

d)

$\sum_{n=1}^3-3\left(2\right)^{n-1}$

e)

$\sum_{n=1}^3-3\left(2\right)^n$

7.

Find the sum of the finite geometric sequence. $\sum_{n=1}^{10}\left(-\frac{3}{4}\right)^{n-1}$

a)

$\frac{1225723}{262144}$

b)

$\frac{141361}{262144}$

c)

$\frac{1068259}{262144}$

d)

$-\frac{1225723}{262144}$

e)

$-\frac{1068259}{262144}$

8.

Write the first five terms of the geometric sequence. $a_1=-5,\ r=\frac{1}{8}$

a)

$-5,\ -\frac{5}{8},\ -\frac{5}{64},\ -\frac{5}{512},\ -\frac{5}{4096}$

b)

$1,\ -5,\ -\frac{5}{8},\ -\frac{5}{64},\ -\frac{5}{512}$

c)

–5, –40, –320, –2,560, –20,480

d)

–5, 3, 11, 19, 27

e)

$-\frac{5}{8},\ -\frac{5}{64},\ -\frac{5}{512},\ -\frac{5}{4096},\ -\frac{5}{32768}$

9.

A principal of $4000 is invested at 8% interest. Find the amount after 10 years if the interest is compounded quarterly.

a)

$8835.16

b)

$8833.16

c)

$8836.16

d)

$8834.16

e)

$8832.16

10.

Find the sum of the finite geometric sequence. $\sum_{n=1}^72^{n-1}$

a)

43

b)

22

c)

127

d)

63

e)

31

11.

Find the indicated nth term of the geometric sequence.

22th term : 8, 32, 128, .....

a)

35,184,372,088,832

b)

549,755,813,888

c)

2,199,023,255,552

d)

8,796,093,022,208

e)

140,737,488,355,328

12.

Write an expression for the nth term of the geometric sequence. Then find the indicated term. (Round your answer to three decimal places.) $a_1=2500,\ r=1.005,\ n=60$

a)

$a_n=\left(1.005\right)^{n-1},\ \ \ About\ 3355.349$

b)

$a_n=2500\left(1.005\right)^{n-1},\ \ \ About\ 3355.349$

c)

$a_n=2500\left(1.005\right)^{n-1},\ \ \ About\ 5520.099$

d)

$a_n=\left(1.005\right)^{n+1},\ \ \ About\ 3355.349$

e)

$a_n=2500\left(1.005\right)^{n+1},\ \ \ About\ 3355.349$

13.

Determine whether the sequence is geometric. If so, find the common ratio. 4, 20, 100, 500, ....

a)

Geometric sequence, r = 4

b)

Geometric sequence, r = 6

c)

Geometric sequence, r = 5

d)

Not a geometric sequence

e)

Geometric sequence, r = 7

14.

Write an expression for the apparent nth term of the sequence. (Assume that n begins with 1.)

1, 7, 13, 19, 25, ....

a)

$a_n=-6n-5$

b)

$a_n=6n-5$

c)

$a_n=5n+6$

d)

$a_n=5n-6$

e)

$a_n=6n+5$

15.

$a_n=-n-2$ Write the first five terms of the sequence. (Assume that n begins with 1.)

a)

–3, –2, –3, –4, –5

b)

–2, –3, –4, –5, –6

c)

–3, –4, –5, –6, –7

d)

–3, –5, –7, –9, –11

e)

1, 0, –2, –2, –3

16.

Write the first five terms of the sequence. Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that n begins with 1.)

a_n = 2 + (n – 2)5

a)

17, 12, 7, 2, –3

Arithmetic sequence

d = –5

b)

–3, 2, 7, 12, 17

Arithmetic sequence

d = 5

c)

–3, 2, 7, 12, 17

Arithmetic sequence

d = –5

d)

32, 27, 22, 17, 12

Arithmetic sequence

d = –5

e)

12, 17, 22, 27, 32

Arithmetic sequence

d = 5

17.

Find a formula for a_nfor the arithmetic sequence.

a₁= 16, d = 6

a)

a_n= –6n + 22

b)

a_n= –6n + 10

c)

a_n= 6n – 10

d)

a_n= 6n + 10

e)

a_n= 6n – 22

18.

Find a formula for a_nfor the arithmetic sequence.

a₃ = 94, a₆ = 87

a)

$a_n=\frac{7}{3}n-101$

b)

$a_n=-\frac{7}{3}n+101$

c)

$a_n=101-303n$

d)

$a_n=\frac{7}{3}n+303$

e)

$a_n=101+303n$

19.

Calculate the binomial coefficient. $7^C4$

a)

33

b)

37

c)

34

d)

36

e)

35

20.

$29^C29$ Calculate the binomial coefficient.

a)

0

b)

4

c)

1

d)

3

e)

2

21.

$\left(x+6\right)^4$ Use the Binomial Theorem to expand and simplify the expression.

a)

$x^4-24x^3+216x^2+864x+1296$

b)

$x^4-24x^3-216x^2+864x+1296$

c)

$x^4-24x^3+216x^2+864x-1296$

d)

$x^4+36x^3-216x^2+864x-1296$

e)

$x^4+24x^3+216x^2+864x+1296$

22.

Find the specified nth term in the expansion of the binomial. $\left(x+y\right)^{10}\ \ ,\ n=6$

a)

$251x^5y^5$

b)

$254x^5y^5$

c)

$253x^5y^5$

d)

$252x^5y^5$

e)

$250x^5y^5$

23.

Find the specified nth term in the expansion of the binomial.
$\left(4a+5b\right)^5\ \ ,\ n=5$

a)

$12500ab^4$

b)

$12500ab^{ }$

c)

$12500a^4b^{ }$

d)

$12500a^4b^4$

e)

$12500a^5b^5$

24.

The probability that a basketball player will make a given free throw is $\frac{6}{10}$ . To find the probability that the player makes exactly 8 out of her next 10 free throws, evaluate the term $10^C8^{\left(\frac{6}{10}\right)^8\left(\frac{4}{10}\right)^2}$ . Round to four decimal places.

a)

0.2721

b)

0.0106

c)

0.0047

d)

0.7558

e)

0.1209

25.

You invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years.

a)

$1,923.23

b)

$10,138.07

c)

$6,701.28

d)

$800.26

26.

Why does the formula for compound interest P = e^rt have no "n" variable?

a)

As the value of n gets higher and higher, the value of (1 + r/n)^rt approaches the value of e, so we substitute in e

b)

The value of n approaches zero in continuous compounding, so we cannot use the compound interest formula

c)

a and b above are both correct

d)

¯\_(ツ)_/¯

27.

How much money do you need to invest at 2.8% compounded continuously in order to have $25,500 at the end of 8 years? Round your answer to the nearest dollar

a)

$20,383

b)

$2,715

c)

$27,147

d)

$2,038

Sequences, Series, Binomial Thm Review

Total questions: 27

Worksheet time: 44mins

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