A sequence as a function that computes an ordered list of numbers. When we add the terms of a sequence, we get a series. When we work with a series, we normally use the summation notation or the sigma notation.

Test Objectives
• Demonstrate the ability to evaluate a series
• Demonstrate the ability to work with summation notation
Introduction to Series Practice Test:

#1:

Instructions: Evaluate each series.

$$a)\hspace{.2em}\sum_{i=1}^{15}(3i - 4)$$

$$b)\hspace{.2em}\sum_{n=1}^{12}(8n - 12)$$

#2:

Instructions: Evaluate each series.

$$a)\hspace{.2em}\sum_{n=1}^{5}(5n - 3)$$

$$b)\hspace{.2em}\sum_{i=1}^{10}(4i - 8)$$

#3:

Instructions: Evaluate each series.

$$a)\hspace{.2em}\sum_{m=1}^{5}(5m + 5)$$

$$b)\hspace{.2em}\sum_{k=1}^{7}(2^{k - 1})$$

#4:

Instructions: Evaluate each series.

$$a)\hspace{.2em}\sum_{m=1}^{9}(-4 \cdot 2^{m - 1})$$

$$b)\hspace{.2em}\sum_{i=1}^{7}(2 \cdot 5^{i - 1})$$

#5:

Instructions: Evaluate each series.

$$a)\hspace{.2em}\sum_{k=2}^{5}(k + 1)^2(k - 3)$$

$$b)\hspace{.2em}\sum_{i=1}^{4}(3i^3 + 2i - 4)$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}300$$

$$b)\hspace{.2em}480$$

#2:

Solutions:

$$a)\hspace{.2em}60$$

$$b)\hspace{.2em}140$$

#3:

Solutions:

$$a)\hspace{.2em}100$$

$$b)\hspace{.2em}127$$

#4:

Solutions:

$$a)\hspace{.2em}-2044$$

$$b)\hspace{.2em}39{,}062$$

#5:

Solutions:

$$a)\hspace{.2em}88$$

$$b)\hspace{.2em}304$$