Exploring Geometric Sequences and Their Formulas

The video tutorial explains geometric sequences, focusing on the concept of a common ratio, which is the factor by which each term is multiplied or divided to get the next term. It covers how to find the common ratio, and introduces both recursive and explicit formulas for geometric sequences. The tutorial includes example problems to demonstrate the application of these formulas, emphasizing the importance of order of operations when using the explicit formula.

What is the common ratio if each term in the sequence is obtained by multiplying the previous term by 2?

• 3

• 2

• 1/2

• 1/4

If a sequence progresses by dividing each term by 2, how should the common ratio be expressed?

• 1/4

• 2

• 1/2

• -1/2

What is the recursive formula for a sequence where each term is three times the previous term, starting from 5?

• a_n = 5 * a_(n-1), a_1 = 3/5

• a_n = 3/5 * a_(n-1), a_1 = 5

• a_n = 5 * a_(n-1), a_1 = 3

• a_n = 3 * a_(n-1), a_1 = 5

What is the explicit formula for a geometric sequence with a first term of 5 and a common ratio of 3?

• a_n = 3 + 5^(n-1)

• a_n = 3 * 5^(n-1)

• a_n = 5 * 3^(n-1)

• a_n = 5 + 3^(n-1)

How would you find the 8th term in a sequence where each term is three times the previous term, starting from 5?

• 5 * 3^7

• 5 + 3^7

• 5 * 3^8

• 3 * 5^7

If the first term of a sequence is 512 and each subsequent term is half of the previous, what is the recursive formula?

• a_n = 512 * a_(n-1), a_1 = 1/2

• a_n = 2 * a_(n-1), a_1 = 512

• a_n = 1/2 * a_(n-1), a_1 = 512

• a_n = 1/2 + a_(n-1), a_1 = 512

What is the explicit formula for a sequence starting at 512 and each term is half the previous term?

• a_n = (1/2) * 512^(n-1)

• a_n = 512 * (1/2)^(n-1)

• a_n = 512 + (1/2)^(n-1)

• a_n = 512 * 2^(n-1)

What would be the 10th term of a sequence starting at 512 with each term being half of the previous term?

• 512 * (1/2)^9

• 512 * 2^9

• 512 + (1/2)^9

• 512 - (1/2)^9

If dividing each term by 2 in a sequence, what is the correct expression for the common ratio?

• 1/2

• 2

• -2

• 1/4

In a geometric sequence, if the common ratio is expressed as a fraction for division, what would be the ratio for dividing by 4?

• 4

• 1/4

• -1/4

• 1/2