Sequences and Series Concepts

The video tutorial explains how to find formulas for alternating sequences. It begins with a simple geometric sequence example, demonstrating how alternating signs can be represented using negative powers. The tutorial then introduces piecewise function notation to express these sequences. It covers sequences with negative initial terms and provides two detailed examples: one arithmetic and one geometric. Each example shows how to derive the formula by considering the absolute value sequence and adjusting for sign alternation. The video emphasizes checking the derived formulas by plugging in values.

What is the initial term of the sequence 1, -1, 1, -1, etc.?

• 0

• 2

• 1

• -1

How do you get from one term to the next in the sequence 1, -1, 1, -1, etc.?

• Add 1

• Multiply by 2

• Multiply by -1

• Subtract 1

What is the formula for the sequence 1, -1, 1, -1, etc.?

• a_n = 1 * (-1)^n

• a_n = (-1)^n

• a_n = n * (-1)^n

• a_n = 1 * n^2

In piecewise function notation, what is a_n when n is even for the sequence 1, -1, 1, -1, etc.?

• n

• 1

• -1

• 0

What is the formula for a sequence starting with -1 and alternating signs?

• a_n = (-1)^n

• a_n = (-1)^(n+1)

• a_n = n * (-1)^n

• a_n = 1 * (-1)^n

What should you find first when dealing with alternating sequences?

• The product of terms

• The absolute value formula

• The difference between terms

• The sum of terms

What is the absolute value sequence of -2, 3, -4, 5, -6, etc.?

• 3, 4, 5, 6, 7

• 0, 1, 2, 3, 4

• 1, 2, 3, 4, 5

• 2, 3, 4, 5, 6

What is the common difference in the absolute value sequence 2, 3, 4, 5, 6, etc.?

• 1

• 0

• 2

• 3

What power of -1 is used in the formula for the sequence -2, 3, -4, 5, -6, etc.?

• n+1

• n

• n-1

• 2n

What is the first term of the sequence 1/2, -2, 8, -32, etc.?

• 1

• 1/2

• -2

• 8