Arithmetic and Geometric SERIES

Arithmetic and Geometric SERIES

To be able to identify a geometric or arithmetic series and find its sum.

Vocabulary Terms to Consider:

• Series: The indicated SUM of the terms of a sequence.

• Finite Series: A series of a sequence with a first term and a last term.

• Infinite Series: A series that continues without end.

• Arithmetic Series: A series whose terms form an arithmetic sequence.

• Geometric Series: A series whose terms form a geometric sequence.

Multiple Choice

Sequence or Series? 2, 4, 6, 8, 10, ...

• Sequence; no addition of terms

• Series; addition of terms

Multiple Choice

Sequence or Series? 2 + 6 + 18 + ...

• Sequence; no addition of terms

• Series; addition of terms

Multiple Choice

Is the following series arithemetic or geometric? Infinite or Finite? 2 + 5 + 8 + 11 + 14 + 17 + 20

• Finite & Arithmetic; it has a last term and has a common difference of 3

• Infinite & Arithmetic; it does not have a last term and has a common difference of 3

• Finite and Geometric; It has a last term and a common ratio of 5:2

• Infinite and Geometric; it does not have a last term but has a common difference of 5:2

Multiple Choice

Is the following series arithemetic or geometric? Infinite or Finite? 1 + 2 + 4 + ...

• Finite & Arithmetic; it has a last term and has a common difference of 2

• Infinite & Arithmetic; it does not have a last term and has a common difference of 2

• Finite and Geometric; It has a last term and a common ratio of 2

• Infinite and Geometric; it does not have a last term but has a common difference of 2

Arithmetic Series

When a series has a finite number of terms you can use a formula using the first and the last term to evaluate the sum. You will NOT have to memorize this formula but write it down for future use in this activity.

Fill in the Blank

Find the sum of the finite arithmetic series; 2 + 4 + 6 + 8 (Use the formula for arithmetic series to verify your results) The sum is ____.

Fill in the Blank

Using the explicit formula for an arithmetic sequence, determine which term 105 is given 7, 14, 21, ..., 105. (Use the explicit formula to solve for "n" given

 $a_n=105$ ) n = ____ 

Fill in the Blank

Given the arithmetic series 7 + 14 + 21 + ... + 105; use the formula from slide 7 to find the sum. The sum is ____.

Fill in the Blank

Find the sum of the finite arithmetic series (-3) + (-6) + (-9) + ... + (-30). You will first need to use the explicit formula to find n given a_n = -30. The sum is ___.

Geometric Series

You can also find the sum of a finite geometric series as long as you know the value of the first term and how many terms (n) are in the series. You will NOT need to memorize this formula, but will need it in future slides, so, write it down.

Multiple Choice

Which of the following is the explicit formula given the geometric sequence 3, 6, 12, ...

• a_n = 3n

• a_n = 3*2^n-1

• a_n = 3ⁿ

• a_n = 2*3^n-1

Fill in the Blank

Given the finite geometric series 3 + 6 + 12 + 24 + ... + 768 what term number (n) is 768? You will need to use the explicit formula to solve for n. n = ____

Fill in the Blank

Use the formula from slide number 12 to find the sum of the geometric series 3 + 6 + 12 + 24 + ... + 768. The sum is ___.

Multiple Choice

Determine if the series is arithmetic or geometric and then evaluate the series for the indicated number of terms. 2 + 4 + 6 + 8 +...; n = 20.

• Arithmetic; Sum = 220

• Arithmetic; Sum = 420

• Geometric; Sum = 1,048,576

• Geometric; Sum = 420

Multiple Choice

Determine if the series is arithmetic or geometric and then evaluate the series for the indicated number of terms. -5 + 25 + -125 + 625 +...; n = 10.

• Arithmetic; Sum = 175

• Arithmetic; Sum = -175

• Geometric; Sum = -12,207,030

• Geometric; Sum = 2,441,406