Quiz about Geometric Sequences Recursive Definition

Question 1

Write the recursive definition for the following geometric sequence:

Accepted Answer

$$a_1=48$$

$$a_n=a_{n-1} imes\left(\frac{3}{2} ight)$$

Answer

$$a_n=48\left(\frac{3}{2}\right)^{n-1}$$

Answer

$$a_n=48\left(\frac{5}{2}\right)^{n-1}$$

Answer

$$a_1=48$$

$$a_n=a_{n-1} imes\left(\frac{5}{3} ight)$$

Question 2

Which geometric sequence matches the recursive definition of:

Accepted Answer

-24, -6, -1.5, -0.375...

Answer

-24, 6, -1.5, 0.375

Answer

-24, 96, -384, 1536

Answer

-24, -96, -384, -1536

Question 3

Given the recursive definition determine the explicit rule:

Accepted Answer

$$a_n=-2\left(8\right)^{n-1}$$

Answer

$$a_n=8\left(-2\right)^n$$

Answer

$$a_n=-2\left(8\right)^n$$

Answer

$$a_n=8\left(-2\right)^{n-1}$$

Question 4

Determine $$a_{15}$$ for the following geometric sequence:

Accepted Answer

0.244141

Answer

0.976562

Answer

0.488281

Answer

0.12207

Question 5

Which formula is used to find the recursive equation for geometric sequences?

Accepted Answer

a_n = a_n-1 * r

Answer

a_n = a_n-1 + d

Answer

a_n = a₁ + d(n-1)

Answer

a_n = a₁ * r^n-1

Question 6

Which recursive formula best describes the sequence
2, -6, 18, - 54...

Accepted Answer

a_n=a_n-1* -3, a₁=2

Answer

a_n=a_n-1* -4, a₁= 2

Answer

a_n=a_n-1* - 8, a₁=2

Answer

a_n=a_n-1* 2, a₁= -3

Question 7

Which formula is the recursive equation for a geometric sequence?

Accepted Answer

Answer

$$a_n=a_1+d\left(n-1\right)$$

Answer

$$a_n=a_1\cdot r^{n-1}$$

Answer

$$a_1=$$
$$a_n=d+a_{n-1}$$

Question 8

Decide whether the sequence is arithmetic, geometric, or neither.

Accepted Answer

geometric

Answer

arithmetic

Answer

neither

Question 9

Decide whether the sequence is arithmetic, geometric, or neither.

Accepted Answer

geometric

Answer

arithmetic

Answer

neither

Question 10

Write the recursive rule of the sequence:::HINT find a(1) use graph or algebra

Accepted Answer

a(1)=72

a(n)=6*a(n-1)

Answer

a(1)=2

a(n)=6*a(n-1)

Answer

a(1)=6

a(n)=2*a(n-1)

Answer

a(1)=2

a(n)=6+a(n-1)

Question 11

Classify this sequence as ARITHMETIC, GEOMETRIC or NEITHER.

-2, 6, -18, 54, . . .

Accepted Answer

GEOMETRIC

Answer

ARITHMETIC

Answer

NEITHER

Question 12

How many terms are in the geometric sequence

2, 6, 18, . . . , 1458

Accepted Answer

n = 7

Answer

n = 5

Answer

n = 6

Answer

n = 486

Geometric Sequences Recursive Definition

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