Given two terms find the nth term of a geometric sequence

The video tutorial explains how to find the 14th term of a geometric sequence given the 4th and 10th terms. It covers the formula for geometric sequences, discusses arithmetic and geometric sequences, and demonstrates how to calculate the common ratio. The tutorial concludes with the calculation of the 14th term and explores alternative methods for finding terms without needing the first term.

What is the formula used to find the nth term in a geometric sequence?

• a_n = a_1 * R^(n-1)

• a_n = a_1 + (n-1)d

• a_n = a_1 / R^(n-1)

• a_n = a_1 * n^R

In a geometric sequence, if you know the 3rd and 1st terms, how can you find the common ratio?

• Add the 3rd term to the 1st term

• Divide the 3rd term by the 1st term

• Subtract the 1st term from the 3rd term

• Multiply the 3rd term by the 1st term

What is the common ratio R if the 6th power of R equals 1/64?

• 1/4

• 1/2

• 1/16

• 1/8

How can you find the 14th term if you know the 10th term and the common ratio?

• Use the formula a_14 = a_10 * 4R

• Use the formula a_14 = a_10 * R^4

• Use the formula a_14 = a_10 + R^4

• Use the formula a_14 = a_10 / R^4

What is the value of the 14th term if the 10th term is 125/64 and the common ratio is 1/2?

• 125/2048

• 125/512

• 125/1024

• 125/256

Why is it not necessary to find the first term when calculating the 14th term from the 10th term?

• Because the 10th term is zero

• Because the sequence is arithmetic

• Because the common ratio is known

• Because the first term is always 1

What is the importance of understanding the relationship between terms in a geometric sequence?

• It helps in finding the sum of the sequence

• It allows for the calculation of any term without the first term

• It is only useful for arithmetic sequences

• It simplifies the process of finding the common difference