Arithmetic and Geometric Sequences

What is the common difference in an arithmetic sequence?

• The sum of all the terms

• The product of all the terms

• The ratio between consecutive terms

• Constant value added or subtracted to each term

Find the next term in the arithmetic sequence: 2, 5, 8, 11, ...

• 17

• 14

• 23

• 20

Find the sum of the first 10 terms in the arithmetic sequence: 3, 7, 11, 15, ...

• 210

• 205

• 220

• 225

What is a geometric sequence?

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

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

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

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

What is the common ratio in a geometric sequence?

• Increasing ratio

• Decreasing ratio

• Constant ratio

• Variable ratio

Find the next term in the geometric sequence: 2, 6, 18, 54, ...

• 81

• 162

• 108

• 216

Find the sum of the first 5 terms in the geometric sequence: 3, 9, 27, 81, ...

• 363

• 243

• 729

• 405

What is the formula to find the nth term of an arithmetic sequence?

• an = a1 + (n-1)d + 1

• an = a1 + nd

• an = a1 + (n+1)d

• an = a1 + (n-1)d

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

• (n/2)(2a + (n+1)d)

• (n/2)(2a + nd)

• (n/2)(2a + (n-1)d)

• (n/2)(2a + (n-2)d)

Which of the following is an arithmetic sequence?

• 2,3,5,8

• 2,7,12,17

• 1,1,2,3,5

• 2,4,8,16