Geometric Sequences and Terms

The video tutorial explains how to calculate specific terms in a geometric sequence using the formula a_n = a_1 * r^(n-1). It covers three examples: calculating the 9th term with a first term of 8 and a common ratio of -3, the 11th term with a first term of 1/100 and a common ratio of 4, and the 8th term with a first term of 55 and a common ratio of 0.25. The tutorial demonstrates using a calculator to find these terms and provides results in both decimal and fractional forms.

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

• a sub n equals a sub 1 times r to the power of n minus 1

• a sub n equals a sub 1 plus r times n

• a sub n equals a sub 1 divided by r to the power of n minus 1

• a sub n equals a sub 1 minus r to the power of n

If the first term of a geometric sequence is 8 and the common ratio is -3, what is the 9th term?

• 16,384

• 8,192

• 24,576

• 52,488

What is the exponent used when calculating the 9th term of the sequence with a common ratio of -3?

• 7

• 8

• 9

• 10

What is the common ratio in the sequence where the first term is 1/100 and the 11th term is calculated?

• 2

• 3

• 4

• 5

How can the 11th term of the sequence with a first term of 1/100 and a common ratio of 4 be expressed?

• 10,485.76 or 262,44/25

• 5,242.88 or 131,22/25

• 20,971.52 or 524,88/25

• 15,728.64 or 393,66/25

In the sequence with a first term of 1/100, what power is the common ratio raised to when calculating the 11th term?

• 11

• 10

• 9

• 8

What is the first term in the sequence where the 8th term is calculated with a common ratio of 0.25?

• 45

• 55

• 75

• 65

What is the common ratio in the sequence where the first term is 55 and the 8th term is calculated?

• 0.15

• 0.20

• 0.25

• 0.30

What is the 8th term of the sequence with a first term of 55 and a common ratio of 0.25?

• 55/2,048

• 55/4,096

• 55/8,192

• 55/16,384

Which calculator is used in the video to compute the terms of the geometric sequences?

• Casio

• Texas Instruments

• Desmos

• HP