Arithmetic and Geometric Sequence

What is the common ratio of the sequence 5, 25, 125?

• 2

• 3

• 5

• 10

What is an arithmetic sequence?

• A sequence of numbers where each term is multiplied by a constant factor.

• A sequence of numbers in which the difference between consecutive terms is constant.

• A sequence of numbers that follows a geometric pattern.

• A sequence of numbers that increases exponentially.

How do you find the common difference in an arithmetic sequence?

• By adding any term to the subsequent term.

• By multiplying any term by a constant factor.

• By subtracting any term from the subsequent term.

• By dividing any term by the first term.

What is the sum of the first n terms of a geometric sequence?

• @@S_n = a_1 \frac{1 - r^n}{1 - r}@@

• @@S_n = a_1 \cdot r^n@@

• @@S_n = \frac{a_1}{1 - r}@@

• @@S_n = n \cdot a_1@@

Is the sequence 17, 9, 1, -7 an arithmetic sequence?

• Yes, the common difference is -8.

• No, the common difference is -6.

• Yes, the common difference is -4.

• No, the common difference is -2.

What is exponential growth?

• Exponential growth occurs when a quantity increases by a constant percentage over equal intervals of time, represented by a geometric sequence.

• Exponential growth is when a quantity decreases by a constant percentage over equal intervals of time.

• Exponential growth refers to a linear increase in quantity over time.

• Exponential growth occurs only in biological populations and not in other contexts.

What is the sum of the first n terms of an arithmetic sequence?

• @@S_n = rac{n}{2} (a_1 + a_n)@@

• @@S_n = n imes a_1@@

• @@S_n = n imes (a_1 + a_n)@@

• @@S_n = rac{n}{2} (a_1 - a_n)@@

What is the formula for the nth term of an arithmetic sequence?

• @@a_n = a_1 + (n-1)d@@

• @@a_n = a_1 + nd@@

• @@a_n = a_1 + (n+1)d@@

• @@a_n = a_1 - (n-1)d@@

What are the next three terms in the arithmetic sequence: -33, -24, -15, -6?

• 3, 12, 21

• 2, 11, 20

• 4, 13, 22

• 1, 10, 19

What is a geometric sequence?

• A sequence of numbers where each term is the sum of the previous two terms.

• A sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

• A sequence of numbers that increases by a fixed amount each time.

• A sequence of numbers that alternates between positive and negative values.