Geometric Sequences and Ratios

The video tutorial explains how to determine the formula for the nth term of a geometric sequence. It begins by introducing the concept of geometric sequences and the importance of the common ratio. The tutorial then derives the formula for the nth term, considering whether the first term is a_0 or a_1. Two methods for finding the common ratio are discussed: analyzing the sequence and using the formula. The video concludes by applying the formula to find the nth term, using the common ratio determined earlier.

What is the first term of the given geometric sequence?

• 320/81

• 9

• 5

• 49

What is the second term of the sequence when n=1?

• 9

• 320/81

• 49

• 5

Which formula is used to find the nth term when the first term is a_0?

• a_n = a * R^n

• a_n = a + R^n

• a_n = a * R^(n-1)

• a_n = a - R^n

What is the common ratio R in a geometric sequence?

• The difference between terms

• The product of terms

• The factor by which each term is multiplied

• The sum of terms

How can you find the common ratio R using the sequence?

• By adding terms

• By subtracting terms

• By multiplying terms

• By dividing a term by the previous term

What is the denominator of the common ratio R in the given sequence?

• 40

• 9

• 8

• 5

What is the numerator of the common ratio R in the given sequence?

• 40

• 5

• 9

• 8

What is the common ratio R for the given sequence?

• 8/9

• 9/8

• 5/9

• 40/9

What is the formula for the nth term of the given sequence?

• a_n = 5 * (9/8)^(n-1)

• a_n = 5 * (8/9)^(n-1)

• a_n = 5 * (9/8)^n

• a_n = 5 * (8/9)^n

What is the value of a when deriving the nth term formula for the given sequence?

• 9

• 40

• 8

• 5