Adding and Subtracting Rational Expressions Explained

The video tutorial by Mr. Winn covers geometric sequences and series, explaining how to find the nth term using a formula. It includes examples of calculating terms, finding explicit equations, and working backwards. The tutorial also covers geometric means, series, and summation of terms, providing practical examples and practice problems.

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

• a_n = a_1 + (n-1)d

• a_n = a_1 * r^(n-1)

• a_n = a_1 * r^n

• a_n = a_1 + r^(n-1)

In the example of social media sharing, what is the common ratio?

• 4

• 3

• 5

• 6

How do you find the common ratio in a geometric sequence?

• Divide the second term by the first term

• Subtract the first term from the second term

• Multiply the first term by the second term

• Add the first term to the second term

If a_4 = 5 and the common ratio is 2, what is a_1?

• 1.25

• 0.625

• 2.5

• 5

What is the value of a_5 if a_1 = 2 and the common ratio is 5?

• 10

• 50

• 250

• 1250

What is the sum of the first 8 terms of a geometric series with a_1 = 5 and r = 5?

• 390625

• 488280

• 600000

• 500000

How do you find the number of terms (n) in a geometric series?

• Top index minus bottom index

• Top index plus bottom index

• Top index minus bottom index plus one

• Top index plus bottom index plus one

What is the sum of the first 8 terms of a geometric series with a_1 = 16 and r = 2?

• 8192

• 4096

• 4080

• 2048

If the sum of the first 7 terms of a geometric series is 131116 and r = 3, what is a_1?

• 12

• 24

• 36

• 48

What is the formula for the sum of the first n terms of a geometric series?

• S_n = a_1 * (1 - r^n) / (1 - r)

• S_n = a_1 * (1 + r^n) / (1 + r)

• S_n = a_1 * (r^n - 1) / (r - 1)

• S_n = a_1 * (r^n + 1) / (r + 1)