Geometric sequences

1003124703

Level:

The second term of a geometric sequence is

15

and the third term is

3

. Find the recursive formula of the sequence.

a_{1} = 75

a_{n + 1} = \frac{1}{5} a_{n}

a_{1} = 3

a_{n + 1} = 5 a_{n}

a_{1} = \frac{3}{5}

a_{n + 1} = \frac{1}{5} a_{n}

a_{1} = \frac{3}{5}

a_{n + 1} = 5 a_{n}

a_{1} = 27

a_{n + 1} = a_{n} - 12

1003124704

Level:

The

10

th term of a geometric sequence is

1

and the

15

th term is

- 1

. Find the recursive formula of the sequence.

a_{1} = - 1

a_{n + 1} = - a_{n}

a_{1} = 1

a_{n + 1} = - a_{n}

a_{1} = - 1

a_{n + 1} = a_{n}

a_{1} = 1

a_{n + 1} = a_{n}

a_{1} = - 1

a_{n + 1} = a_{n} - 1

1003124705

Level:

The third term of a geometric sequence is

3

and the common ratio is

3

. Find the

n

th term.

a_{n} = 3^{n - 2}

n \in N

a_{n} = 3^{n - 1}

n \in N

a_{n} = 3^{n}

n \in N

a_{n} = \frac{3}{n}

n \in N

a_{n} = 3 n

n \in N

1003124706

Level:

The first term of a geometric sequence is

5

and the fourth term is

40

. Find the

n

th term.

a_{n} = 5 \cdot 2^{n - 1}

n \in N

a_{n} = \frac{5 n}{2}

n \in N

a_{n} = 5 \cdot 2^{n}

n \in N

a_{n} = 5 n

n \in N

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

n \in N

1003124707

Level:

The

n

th term of a geometric sequence is

2 \cdot 3^{n - 2}

. Find the third term and the common ratio.

a_{3} = 6

q = 3

a_{3} = 3

q = - 2

a_{3} = 6

q = - 3

a_{3} = 6

q = 2

a_{3} = 3

q = 6

1003124708

Level:

The

n

th term of a geometric sequence is

3^{n - 1} \cdot 2^{n + 1}

. Find the second term and the common ratio.

a_{2} = 24

q = 6

a_{2} = 6

q = 6

a_{2} = 2

q = 3

a_{2} = 24

q = 2

a_{2} = 3

q = 3

1003134601

Level:

The fifth term of a geometric sequence is

4 \sqrt{2}

and the second term is

2

. Find the fourth term.

4

2 \sqrt{2}

3 \sqrt{2}

\sqrt{2}

2

2000014011

Level:

The picture shows a part of the graph of a geometric sequence. What is the common ratio of the geometric sequence?

- \frac{1}{2}

- 2

\frac{1}{2}

{(- \frac{1}{2})}^{n}

2010004903

Level:

The seventh term of a geometric sequence is

32

and the tenth term is

4

. Choose the correct formula to find the eighth term of this sequence.

a_{8} = 32 \cdot \sqrt[3]{\frac{4}{32}}

a_{8} = 32 \cdot \sqrt[3]{\frac{32}{4}}

a_{8} = 4 \cdot \sqrt[3]{\frac{4}{32}}

a_{8} = 4 \cdot \sqrt[3]{\frac{32}{4}}

a_{8} = 8 \cdot \sqrt[3]{\frac{3}{24}}

2010004904

Level:

The

n

th term of a geometric sequence is

\frac{2}{9}

, the common ratio is

\frac{1}{3}

and the fourth term is

6

. Find

n

7

8

6

10

5

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