Free Printable Sequence and Trigonometry

1.

State if the sequence 1,9, 25, 49, 81, ... is arithmetic, geometric, or neither.

a)

Geometric

b)

Arithmetic

c)

Neither

2.

State if the sequence -4, 8, -16, 32, -64, ... is arithmetic, geometric, or neither.

a)

Geometric

b)

Arithmetic

c)

Neither

3.

Which statement is true about this formula?

a)

It is an EXPLICIT formula. The first four terms are 5,7,9,11

b)

It is a RECURSIVE formula. The first four terms are 5,13,29,61

c)

It is an EXPLICIT formula. The first four terms are 13,15,17,19

d)

It is a RECURSIVE formula. The first four terms are 13,29,61,125

4.

Which statement is true about this formula?

a)

It is an EXPLICIT formula. The first four terms are -1,2,7,14

b)

It is a RECURSIVE formula. The first four terms are -2,2,0,-2

c)

It is an EXPLICIT formula. The first four terms are -1,-3,7,47

d)

It is a RECURSIVE formula. The first four terms are -2,-6,-18,-36

5.

Which of the following represents the series 2+5+8+11+14+17+20?

a)

b)

c)

d)

6.

a)

2400

b)

2450

c)

4800

d)

9700

7.

What is the rule for the nth term of the geometric sequence describe above?

a)

b)

c)

d)

8.

How many terms are in the geometric series described above?

a)

5

b)

6

c)

7

d)

8

9.

The sum of the geometric series

a)

b)

c)

8880

d)

There is no sum because it never ends.

10.

Find the sum of the infinite geometric series, if it exists. $\sum_{n=1}^{\infty}8\left(\frac{1}{5}\right)^{n-1}$

a)

8

b)

8/5

c)

10

d)

Does not exist

11.

Write the explicit formula for the arithmetic sequence. $a_1=30\ \ \ and\ \ \ \ d=4.$

a)

$a_n=4n+26$

b)

$a_n=4n$

c)

$a_n=4n+30$

d)

$a_n=30\left(4\right)^{n-1}$

12.

Which of the following is false?

a)

$\sin\left(-x\right)=-\sin\left(x\right)$

b)

$\cos\left(-x\right)=-\cos\left(x\right)$

c)

$\tan\left(-x\right)=-\tan\left(x\right)$

d)

$\cot\left(-x\right)=-\cot\left(x\right)$

13.

Simplify: $\left(\cos x-\sin x\right)^2$

a)

$1$

b)

$\cos2x$

c)

$\cos2x+\sin2x$

d)

$1-\sin2x$

14.

Which of the following is false?

a)

$\sin\left(a+b\right)=\sin a\cos b-\cos a\sin b$

b)

$\cos\left(a-b\right)=\cos a\cos b+\sin a\sin b$

c)

$\tan\left(a+b\right)=\frac{\tan a+\tan b}{1-\tan a\tan b}$

d)

$\tan\left(a-b\right)=\frac{\tan a-\tan b}{1+\tan a\tan b}$

15.

Simplify: $\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)$

a)

$\cos x$

b)

$\frac{\cos x}{2}$

c)

$\sin x$

d)

$\frac{\sin x}{2}$

16.

If $3\sin x-3\sqrt[]{3}\cos x=R\ \sin\left(x-\alpha\right)$ , what is the value of R?

a)

$3$

b)

$6$

c)

$3\sqrt[]{2}$

d)

$36$

17.

If $3\sin x-3\sqrt[]{3}\cos x=R\ \sin\left(x-\alpha\right)$ , what is the value of $\alpha$ ?

a)

$\frac{\pi}{3}$

b)

$\frac{\pi}{6}$

c)

$\frac{\pi}{4}$

d)

$-\frac{\pi}{3}$

18.

What is the maximum value of $5\sin\left(2x\right)+12\cos\left(2x\right)$

a)

5

b)

12

c)

17

d)

13

19.

What is the maximum value of $\left[4\sin\left(2x-1\right)-2\sqrt[]{6}\cos\left(2x-1\right)\right]^2$

a)

16

b)

24

c)

40

d)

6

20.

What is the minimum value of $\left[4\sin\left(2x-1\right)-2\sqrt[]{6}\cos\left(2x-1\right)\right]^2$

a)

16

b)

24

c)

-40

d)

0

Sequence and Trigonometry

Total questions: 20

Worksheet time: 1hrs 21mins

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