Exploring Geometric Sequences and Series

This video tutorial covers geometric sequences and series, explaining how to identify them, find common ratios, and use formulas to determine terms. It also discusses calculating the sum of both finite and infinite geometric sequences, providing examples and shortcuts for efficient problem-solving.

What distinguishes a geometric sequence from an arithmetic sequence?

• Each term is subtracted by a constant to get the next term.

• Each term is the sum of all previous terms.

• The ratio between consecutive terms is constant.

• The difference between consecutive terms is constant.

In a geometric sequence, if the first term is 3 and the common ratio is 2, what is the third term?

• 15

• 6

• 9

• 12

If the common ratio of a geometric sequence is -1/2, what is the sign of the third term if the first term is positive?

• Cannot be determined

• Positive

• Negative

• Zero

In a geometric sequence, if the second term is 10 and the common ratio is 5, what is the first term?

• 5

• 50

• 0.5

• 2

How do you find the nth term of a geometric sequence?

• Subtract the common ratio from the first term n times.

• Divide the first term by the common ratio raised to the power of n.

• Add the common ratio to the first term n times.

• Multiply the first term by the common ratio raised to the power of (n-1).

What is the sum of the first 5 terms of a geometric sequence with a first term of 2 and a common ratio of 3?

• 486

• 242

• 121

• 363

What formula is used to find the sum of the first n terms in a geometric series?

• First term divided by (1 - ratio^n)

• Sum of squares of the first n terms

• First term plus ratio multiplied by n

• First term multiplied by (1 - ratio^n) divided by (1 - ratio)

Which condition must be met for an infinite geometric series to converge?

• The common ratio must be less than 1.

• The common ratio must be greater than 1.

• The first term must be 1.

• The series must have a finite number of terms.

If the first term of an infinite geometric series is 8 and the common ratio is 1/3, what is the sum of the series?

• 20

• 12

• 24

• 8

What is the sum of an infinite geometric series with a first term of 7 and a common ratio of 1/2?

• 21

• 7

• 14

• 28