Understanding Alternating Sequences

The video tutorial explains how to determine terms in a sequence defined by a formula involving alternating powers of negative one. It covers calculating initial terms, understanding the alternating nature of the sequence, and determining higher terms like the 99th and 100th. The sequence alternates between 7 and 9 based on whether the exponent is odd or even.

What is the value of the first term in the sequence given by a_n = 8 + (-1)^n?

• 7

• 6

• 9

• 8

How is the second term of the sequence calculated?

• By adding 8 to the cube of -1

• By adding 8 to -1

• By adding 8 to the square of -1

• By subtracting 1 from 8

What is the value of the third term in the sequence?

• 8

• 7

• 6

• 9

What is the result of raising -1 to the fourth power?

• -1

• 0

• 1

• 2

What pattern is observed in the sequence when the exponent is odd?

• The result is always 0

• The result is always 2

• The result is always 1

• The result is always -1

What is the value of the 99th term in the sequence?

• 6

• 7

• 8

• 9

How is the 99th term calculated using the pattern?

• By adding 8 to 1

• By subtracting 1 from 8

• By adding 8 to -1 raised to an odd power

• By adding 8 to the square of -1

What is the value of the 100th term in the sequence?

• 9

• 6

• 7

• 8

How is the 100th term calculated using the pattern?

• By adding 8 to -1 raised to an even power

• By adding 8 to the cube of -1

• By subtracting 1 from 8

• By adding 8 to -1

What is the name of the sequence where terms alternate between two values?

• Fibonacci sequence

• Alternating sequence

• Geometric sequence

• Arithmetic sequence