Geometric Sequences and Common Ratios

The video tutorial explains how to find specific terms in geometric sequences using a formula. It covers two examples: finding the seventh term of a sequence with a common ratio of 4 and the fifth term of another sequence with a common ratio of 2.5. The process involves identifying the first term and the common ratio, then applying the formula a_n = a_1 * r^(n-1) to calculate the desired term. The tutorial also demonstrates how to verify the common ratio by dividing consecutive terms.

What is the first term of the geometric sequence given in the first example?

• -8

• -32

• -128

• 4

How do you determine the common ratio in a geometric sequence?

• By subtracting the first term from the second term

• By adding the first term to the second term

• By dividing any term by the previous term

• By multiplying the first term by the second term

What is the common ratio of the sequence: -8, -32, -128?

• -4

• 4

• -8

• 8

Using the formula for the nth term, what is the exponent when finding the seventh term?

• 5

• 6

• 7

• 8

What is the seventh term of the sequence: -8, -32, -128?

• -32768

• -16384

• -4096

• -8192

What is the first term of the second sequence: 9, 22.5, 56.25?

• 2.5

• 56.25

• 22.5

• 9

How is the common ratio calculated for the sequence: 9, 22.5, 56.25?

• By multiplying 9 by 22.5

• By subtracting 9 from 22.5

• By dividing 22.5 by 9

• By adding 9 to 22.5

What is the common ratio of the sequence: 9, 22.5, 56.25?

• 2

• 2.5

• 3

• 3.5

What is the exponent used when calculating the fifth term of the sequence: 9, 22.5, 56.25?

• 3

• 4

• 5

• 6

What is the fifth term of the sequence: 9, 22.5, 56.25?

• 351.5625

• 312.5

• 375

• 400