Arithmetic and Geometric Sequences

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

• d = a_n - a_(n-1)

• d = a_(n+1) - a_n

• d = a_n + a_(n-1)

• d = a_(n-1) - a_n

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.

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

• S_n = n/2 * (a_1 + a_n)

• S_n = n * a_1

• S_n = a_n - a_1

• S_n = n * (a_1 + a_n)/2

What is the next term in the geometric sequence 2, 6, 18, 54?

• 108

• 162

• 216

• 54

What is the formula for the nth term of a geometric sequence?

• a_n = a_1 * r^(n-1)

• a_n = a_1 + (n-1) * r

• a_n = a_1 / r^(n-1)

• a_n = r^n * a_1

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.

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

• S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.

• S_n = a_1 * r^n / (1 - r) for r ≠ 1.

• S_n = a_1 * (r^n - 1) / (r - 1) for r ≠ 1.

• S_n = n * a_1 for r = 1.

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

• By adding any term to the previous term: r = a_n + a_(n-1).

• By multiplying any term by the previous term: r = a_n * a_(n-1).

• By dividing any term by the previous term: r = a_(n+1) / a_n.

• By subtracting any term from the previous term: r = a_n - a_(n-1).

What is the next term in the arithmetic sequence 3, 7, 11, 15?

• 15

• 17

• 19

• 21