Arithmetic and Geometric Sequences

The video tutorial explains how to find the nth term in sequences, focusing on arithmetic and geometric sequences. It discusses the differences in arithmetic sequences and explores geometric ratios. The tutorial provides a step-by-step guide to finding the common ratio and calculating the 14th term using known values. It concludes with tips for solving similar problems.

What is the formula for the nth term of a geometric sequence?

• a_n = a_1 * n^(r-1)

• a_n = a_1 + (n-1)d

• a_n = a_1 * r^(n-1)

• a_n = a_1 / r^(n-1)

In an arithmetic sequence, what must be true about the differences between consecutive terms?

• They must be zero.

• They must be equal.

• They must be decreasing.

• They must be increasing.

If given a_3 and a_1 in an arithmetic sequence, how can you find the common difference?

• Subtract a_1 from a_3 and divide by 2.

• Subtract a_1 from a_3 and divide by 3.

• Add a_1 to a_3 and divide by 2.

• Multiply a_1 by a_3 and divide by 2.

What is the relationship between the ratios of consecutive terms in a geometric sequence?

• They must be increasing.

• They must be decreasing.

• They must be equal.

• They must be zero.

How can you find the common ratio (r) if given a_10 and a_4?

• Divide a_10 by a_4 and raise to the power of 6.

• Multiply a_10 by a_4 and raise to the power of 4.

• Divide a_10 by a_4 and raise to the power of 4.

• Multiply a_10 by a_4 and raise to the power of 6.

What is the sixth root of 64?

• 16

• 8

• 2

• 4

What is the common ratio (r) if a_10 = 125/64 and a_4 = 125?

• 1/4

• 1/16

• 1/2

• 1/8

If a_10 = 125/64 and r = 1/2, what is a_14?

• 125/256

• 125/1024

• 125/512

• 125/2048

How do you find a_14 if you know a_10 and r?

• Divide a_10 by r^10

• Multiply a_10 by r^10

• Divide a_10 by r^4

• Multiply a_10 by r^4

What is the value of 1/2 raised to the fourth power?

• 1/64

• 1/32

• 1/8

• 1/16