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Resources

Geometric sequences

13^{\text {th }}

term of the geometric sequence

3,-12,48, \ldots

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11^{\text {th }}

term of the geometric sequence

1,2,4, \ldots

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10^{\text {th }}

term of the geometric sequence

9,45,225, \ldots

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0.6, 0.7, 0.5, 0.3, 0.15

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Find the range:

34782

\times

549

Find the wrong number in the following series:

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3, 12, 16, 80, 85, 504, 516

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12

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16

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504

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516

Complete the recursive formula of the geometric sequence

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\begin{array}{l} -0.56,-5.6,-56,-560, \ldots . \\ c(1)=\square \\ c(n)=c(n-1) \cdot \square \end{array}

Complete the recursive formula of the geometric sequence

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16,3.2,0.64,0.128, \ldots \text {. }

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a(1)= \square

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a(n)=a(n-1) \cdot \square

Complete the recursive formula of the geometric sequence

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\begin{array}{l} -125,-25,-5,-1, \ldots . \\ b(1)=\square \\ b(n)=b(n-1) \cdot \square \end{array}

f(n)=45 \cdot\left(\frac{4}{5}\right)^{n-1}

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Complete the recursive formula of

f(n)

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\begin{array}{l} f(1)=\square \\ f(n)=f(n-1) \cdot \square \end{array}

Complete the recursive formula of the geometric sequence

0.2,-1,5,-25, \ldots

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a(1)= \square

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a(n)=a(n-1) \cdot \square

Complete the recursive formula of the geometric sequence

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\begin{array}{l} -0.25,-2,-16,-128, \ldots . \\ b(1)=\square \\ b(n)=b(n-1) \cdot \square \end{array}

f(n)=2 \cdot(-3)^{n}

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Complete the recursive formula of

f(n)

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\begin{array}{l} f(1)=\square \\ f(n)=f(n-1) \cdot \square \end{array}

Complete the recursive formula of the geometric sequence

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27,-9,3,-1, \ldots \text {. }

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b(1)=\square

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b(n)=b(n-1) \cdot \square

Woo-Jin and Kiran were asked to find an explicit formula for the sequence

64,16,4,1, \ldots

, where the first term should be

f(1)

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Woo-Jin said the formula is

f(n)=64 \cdot\left(\frac{1}{4}\right)^{n}

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Kiran said the formula is

f(n)=16 \cdot\left(\frac{1}{4}\right)^{n-1} .

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Which one of them is right?

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1

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(A) Only Woo-Jin

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(C) Both Woo-Jin and Kiran

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(D) Neither Woo-Jin nor Kiran

f(n)=5 \cdot(-2)^{n-1}

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Complete the recursive formula of

f(n)

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\begin{array}{l} f(1)=\square \\ f(n)=f(n-1) \cdot \square \end{array}

f(n)=-48 \cdot\left(-\frac{1}{4}\right)^{n}

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Complete the recursive formula of

f(n)

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\begin{array}{l} f(1)=\square \\ f(n)=f(n-1) \cdot \square \end{array}

h(n)=-91 \cdot\left(-\frac{1}{7}\right)^{n-1}

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Complete the recursive formula of

h(n)

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\begin{array}{l} h(1)=\square \\ h(n)=h(n-1) \cdot \square \end{array}

Find an explicit formula for the geometric sequence

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2,6,18,54, \ldots \text {. }

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Note: the first term should be

b(1)

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b(n)=\square

Complete the recursive formula of the geometric sequence

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\begin{array}{l} -0.1,-0.5,-2.5,-12.5, \ldots . \\ c(1)=\square \\ c(n)=c(n-1) \cdot \square \end{array}

h(n)=-15 \cdot 6^{n}

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Complete the recursive formula of

h(n)

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\begin{array}{l} h(1)=\square \\ h(n)=h(n-1) \cdot \square \end{array}

h(n)=63 \cdot\left(-\frac{1}{3}\right)^{n}

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Complete the recursive formula of

h(n)

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\begin{array}{l} h(1)=\square \\ h(n)=h(n-1) \cdot \square \end{array}

g(n)=80 \cdot\left(\frac{3}{4}\right)^{n}

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Complete the recursive formula of

g(n)

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g(1)= \square

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g(n)=g(n-1) \cdot \square

Complete the recursive formula of the geometric sequence

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\begin{array}{l} -0.3,0.9,-2.7,8.1, \ldots . \\ b(1)=\square \\ b(n)=b(n-1) \cdot \square \end{array}

g(n)=-11 \cdot 4^{n}

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Complete the recursive formula of

g(n)

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g(1)= \square

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g(n)=g(n-1) \cdot \square

g(n)=-72 \cdot\left(\frac{1}{6}\right)^{n-1}

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Complete the recursive formula of

g(n)

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\begin{array}{l} g(1)=\square \\ g(n)=g(n-1) \cdot \square \end{array}

Which of the following numbers are greater than

-0

33

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Choose all answers that apply:

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-0

3

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-\frac{3}{9}

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\frac{1}{6}

\sum_{k=0}^{19}-4(-2)^{k} \approx

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1

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-699,052

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1,398,100

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2,097,152

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4,194,308

Find the sum of the first

35

terms in this geometric series:

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8-12+18 \text {. . }

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1

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-8.69 \cdot 10^{30}

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-3,106,363.96

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4,659,553.94

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7,765,917.90

11 \%

x

66

, what is the value of

x

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1

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660

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600

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77

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6

a(n)=\frac{3}{2}(-2)^{n-1}

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3^{\text {rd }}

term in the sequence?

d(n)=\frac{5}{16}(2)^{n-1}

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5^{\text {th }}

term in the sequence?

d(n)=-5\left(\frac{1}{2}\right)^{n-1}

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3^{\text {rd }}

term in the sequence?

a(n)=-\frac{1}{16}(2)^{n-1}

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4^{\text {th }}

term in the sequence?

\left\{\begin{array}{l} a(1)=-11 \\ a(n)=a(n-1) \cdot 10 \end{array}\right.

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4^{\text {th }}

term in the sequence?

\left\{\begin{array}{l} d(1)=8 \\ d(n)=d(n-1) \cdot(-5) \end{array}\right.

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3^{\text {rd }}

term in the sequence?

\left\{\begin{array}{l} b(1)=15 \\ b(n)=b(n-1) \cdot(-3) \end{array}\right.

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4^{\text {th }}

term in the sequence?

c(n)=-6\left(-\frac{1}{3}\right)^{n-1}

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2^{\text {nd }}

term in the sequence?

c(n)=-\frac{9}{2}\left(-\frac{4}{3}\right)^{n-1}

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2^{\text {nd }}

term in the sequence?

b(n)=1(-2)^{n-1}

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4^{\text {th }}

term in the sequence?

\left\{\begin{array}{l} d(1)=\frac{1}{12} \\ d(n)=d(n-1) \cdot(-6) \end{array}\right.

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4^{\text {th }}

term in the sequence?

\left\{\begin{array}{l} a(1)=20 \\ a(n)=a(n-1) \cdot \frac{3}{2} \end{array}\right.

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3^{\text {rd }}

term in the sequence?

\left\{\begin{array}{l} c(1)=56 \\ c(n)=c(n-1) \cdot \frac{1}{2} \end{array}\right.

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4^{\text {th }}

term in the sequence?

\left\{\begin{array}{l} b(1)=-54 \\ b(n)=b(n-1) \cdot \frac{4}{3} \end{array}\right.

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4^{\text {th }}

term in the sequence?

\left\{\begin{array}{l} b(1)=-500 \\ b(n)=b(n-1) \cdot \frac{4}{5} \end{array}\right.

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3^{\text {rd }}

term in the sequence?

\left\{\begin{array}{l} c(1)=\frac{3}{16} \\ c(n)=c(n-1) \cdot 4 \end{array}\right.

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3^{\text {rd }}

term in the sequence?

\left\{\begin{array}{l} a(1)=\frac{5}{3} \\ a(n)=a(n-1) \cdot(-9) \end{array}\right.

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3^{\text {rd }}

term in the sequence?

b(n)=-1(2)^{n-1}

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5^{\text {th }}

term in the sequence?

d(n)=3(-2)^{n-1}

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4^{\text {th }}

term in the sequence?

c(n)=\frac{4}{9}(-3)^{n-1}

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3^{\text {rd }}

term in the sequence?

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