Alternating Sequences and Their Rules

The video tutorial explains how to determine the rule for a sequence with alternating signs. It begins by identifying the need to incorporate negative one raised to the power of n to account for the alternating signs. The instructor then adjusts the formula to ensure the first term is positive by adding one. After resolving the alternating signs, the focus shifts to finding the rule for the sequence by relating the sequence number to its value, ignoring the signs. The rule is determined by multiplying the sequence number by two.

What is the first step in solving a problem involving alternating sequences?

• Check for even numbers

• Identify the sequence pattern

• Determine the rule U

• Calculate the first term

Why is (-1)^n used in sequences?

• To alternate the signs

• To increase the sequence value

• To make the sequence even

• To decrease the sequence value

What is the role of (-1)^n in the sequence?

• To make the sequence longer

• To decrease the sequence value

• To alternate the signs

• To increase the sequence value

How can you ensure the first term of an alternating sequence is positive?

• Subtract one from n

• Add one to n

• Multiply n by two

• Divide n by two

What is the effect of adding one to n in the context of alternating sequences?

• It makes the sequence even

• It ensures the first term is positive

• It decreases the sequence value

• It has no effect

What is the significance of the sequence's first term being positive?

• It indicates the sequence is increasing

• It ensures the sequence starts correctly

• It makes the sequence easier to calculate

• It has no significance

What happens when you raise (-1) to an odd power?

• The result is positive

• The result is undefined

• The result is zero

• The result is negative

What is the purpose of resolving alternating signs in a sequence?

• To ensure the sequence alternates correctly

• To simplify the sequence

• To make all terms negative

• To make all terms positive

What is the result of raising (-1) to an even power?

• The result is positive

• The result is undefined

• The result is zero

• The result is negative

How do you ensure the sequence alternates correctly?

• By subtracting one from each term

• By multiplying each term by two

• By using (-1)^n

• By adding a constant to each term