Free Printable Quiz 5.3 Series and Summation

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Quiz 5.3 Series and Summation

Total questions: 42

Worksheet time: 2hrs 0mins

Name

Class

Date

This symbol is:

a funky looking "E"

theta

sigma

Write an explicit formula for a_n, the nth term of the sequence 9, 13, 17, ...

a_n = 9 + 4(n-1)

a_n = 9 - 4(n-1)

a_n = 9 + 4(n)

a_n = 9 * 4^n-1

In a geometric sequence, what does r represent?

(a)

Find the common ratio of the geometric sequence 11, -55, 275,...

Write an explicit formula for a_n, the nth term of the sequence 63, -21, 7, ...

a_n = 63 - 84(n-1)

a_n = 63 * (1/3)^n-1

a_n = 63 * (-1/3)^n-1

a_n = 63 * (-3)^n-1

The series is written in summation notation, what is the value of the term when the index, k, equals 3?

(a)

A convergent sequence is.......

A vertical asymptote

A set of numbers that don't approach a specific value

A set of numbers that stay constant

A set of numbers that approach a specific value

A divergent sequence is.......

A vertical asymptote

A set of numbers that don't approach a specific value

A set of numbers that stay constant

A set of numbers that approach a specific value

Find the sum for the following series.

10.

Find the sum for the following series.

11.

-21, -16, -11, -6, ...

Is this sequence arithmetic, geometric, or neither?

arithmetic (common difference d = 5)

geometric (common ratio r = 5)

neither

12.

Find the geometric sum

13.

Determine if the series converges or diverges

Converges

Diverges

14.

You have $10 in you bank account. It doubles every month. How much money will you have after 5 months?

15.

Is this sum finite or infinite?

Finite, because there are 4 terms to add up.

Infinite, because there are an infinite amount of terms to add up (m goes from 1 to infinity).

16.

a₁=2, r=−2, Sn = 22

Determine the number of terms n in the series

17.

Determine the sum of the series.

18.

Find the sum: 3 + 8 + 13 + 18 + … + 98

19.

Write in summation notation: 17 + 15 + 13 + …. + (-7)

(a)

20.

Which of the following gives the formula for the first 7 terms of the series:

3 + 6 + 12 + 24 +...

$3\left(\frac{1-\left(2\right)^7}{1-2}\right)$

$2\left(\frac{1-\left(3\right)^7\ }{1-2}\right)$

$\frac{7}{2}\left(2+15\right)$

$\frac{7}{2}\left(3+192\right)$

21.

Is the series below converging or diverging?

20 + 10 + 5 + 2.5....

Converging because the common ratio is greater than 1

Converging because the common ratio is less than 1

Diverging because the common ratio is greater than 1

Diverging because the common ratio is less than 1

22.

Evaluate the infinite series described:

(a)

23.

Name the given sequence

Converge Geometric Series

Diverge Geometric Series

Infinite Arithmetic Sequence

Arithmetic Series

24.

You are sitting in row 23 and notice there are 65 seats in your row. The row in front of you has 63 seats and the row behind you has 67 seats. There are 42 rows in the auditorium. How many seats does the auditorium contain? (Hint: Find the number of seats in the first and last rows)

25.

The summation is the same as which series?

(4+10) + (4+20) + (4+30) + (4+40) + (4+50) + (4+60) + (4+70) + (4+80) + (4+90) + (4+100) + (4+110)

1+2+3+4+5+6+7+8+9+10+11

4 + 110

4 + 10

26.

A bathroom floor has tiles arranged in 9 circles. The innermost circle contains 9 tiles. Each successive circle contains 9 more tiles than the previous circle. How many total tiles are on the bathroom floor?

27.

Every hour a clock chimes as many times as the hour. How many times does it chime from 1 A.M. to midnight, inclusive?

28.

The front row of a theater has 25 seats. Each of the rows behind it has two more seats than the row before it. How many total seats are there in the first 20 rows?

29.

Which of the following series that converge.

30.

Which of the following statement is TRUE.

If the partial sums of a sequence form an arithmetic sequence, then the original sequence must be constant.

A convergent infinite geometric series always has a sum less than 1.

If two different series have the same sum, then their corresponding terms must be equal.

The process of finding a closed-form expression for a finite summation is always possible using algebraic manipulation.

31.

Which of the following statement is not true?

An alternating series with decreasing terms and a limit of zero always converges.

Sigma notation can only be used for arithmetic series.

The sum of a geometric series can be negative.

The sigma notation

means 1 + 2 + 3 + 4.

32.

A new colony of carpenter ants collects 48 leaves on the 11st day, 57.6 leaves on the 2nd day, 69.12 leaves on the 3rd day, and so on. Each day they collect 120% of the previous day's amount. How many leaves will they collect in total over 10 days? Round your answer to the nearest whole number.

The total number of leaves can be found using the formula for the sum of a finite geometric series:

33.

Find the sum of the first 55 terms of the geometric sequence.

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

34.

Which of the following series is not a divergent series?

35.

Angus makes $53,000 in his 11st year working, $57,000 in his 2nd year, $61,000 in his 3rd year, and so on. Assume the pattern continues. After 10 years working, how much will Angus make in total?

36.

A ball is thrown 12 meters in the air (so that the initial up-and-down distance is 24 meters). The ball rebounds 95% of the distance it falls. What is the total vertical distance traveled by the ball before it stops bouncing?

37.