Understanding Geometric Sequences

The video tutorial explains how to determine the first five terms of a geometric sequence with a given first term and common ratio. It introduces the formula for geometric sequences and demonstrates two methods for calculating terms: using the previous term and using the formula directly. The tutorial provides step-by-step calculations for each method, ensuring the same results are achieved. The video concludes with a recap of the methods used.

What is the first term of the sequence given in the problem?

• 7

• 3

• 1

• 5

Tags

CCSS.HSF.BF.A.2

What is the common ratio of the sequence?

• -2

• -3

• -5

• -4

Tags

CCSS.HSF.BF.A.2

Which formula represents the nth term of a geometric sequence?

• A sub n = A sub 1 + R^(n-1)

• A sub n = A sub 1 * R^(n-1)

• A sub n = A sub 1 / R^(n-1)

• A sub n = A sub 1 - R^(n-1)

Tags

CCSS.HSF.BF.A.2

How do you calculate the second term of the sequence using the recursive method?

• Multiply the first term by 2

• Multiply the first term by the common ratio

• Add the common ratio to the first term

• Subtract the common ratio from the first term

Tags

CCSS.HSF.BF.A.2

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

• -48

• 48

• -12

• 12

Tags

CCSS.HSF.BF.A.2

What is the fourth term of the sequence when calculated recursively?

• -192

• 192

• 48

• -48

Tags

CCSS.HSF.BF.A.2

How is the fifth term calculated using the explicit formula?

• 3 * (-4)^5

• 3 * (-4)^3

• 3 * (-4)^2

• 3 * (-4)^4

Tags

CCSS.HSF.BF.A.2

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

• 192

• 768

• -192

• -768

Tags

CCSS.HSF.BF.A.2

Which method is faster for finding consecutive terms in a geometric sequence?

• Using the explicit formula

• Using the recursive method

• Using both methods simultaneously

• Neither method is faster

Tags

CCSS.HSF.BF.A.2

What is the main takeaway from the video regarding geometric sequences?

• The recursive method is always better

• Both methods yield the same results

• Geometric sequences are unpredictable

• The explicit formula is more accurate

Tags

CCSS.HSF.BF.A.2