Math Sequences

What is the common difference in the arithmetic sequence: 3, 7, 11, 15, ...?

• 2

• 3

• 4

• 5

Tags

CCSS.HSF.BF.A.2

• 25

• 28

• 29

• 30

Tags

CCSS.HSF.BF.A.2

If the first term of an arithmetic sequence is 8 and the 10th term is 44, what is the common difference?

• 3.6

• 4

• 4.5

• 5

Tags

CCSS.HSF.BF.A.2

• 1

• 2

• 3

• 4

Tags

CCSS.HSF.BF.A.2

The sum of the first 10 terms of an arithmetic sequence is 145. If the first term is 5, what is the common difference?

• 1.5

• 2

• 2.5

• 3

What is an arithmetic sequence?

• An arithmetic sequence is a sequence of numbers with a constant difference between consecutive terms.

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

• A random sequence of numbers without any specific pattern.

• A sequence that only includes prime numbers.

Answer explanation

An arithmetic sequence is defined by a constant difference between consecutive terms, making the first answer choice correct. The other options describe different types of sequences or lack a specific pattern.

Tags

CCSS.HSF.BF.A.2

What is the 10th term of the arithmetic sequence defined by the first term a₁=4 and a common difference d=3?

• 31

• 25

• 34

• 28

Answer explanation

To find the 10th term of the arithmetic sequence, use the formula a_n = a₁ + (n-1)d. Here, a₁ = 4, d = 3, and n = 10. Thus, a₁ + (10-1)3 = 4 + 27 = 31. Therefore, the 10th term is 31.

Tags

CCSS.HSF.BF.A.2

If the first term of an arithmetic sequence is 7 and the common difference is -2, what is the 5th term?

• 5

• -1

• 3

• -5

Answer explanation

To find the 5th term of the sequence, use the formula: a_n = a_1 + (n-1)d. Here, a_1 = 7, d = -2, and n = 5. So, a_5 = 7 + (5-1)(-2) = 7 - 8 = -1. Thus, the 5th term is -1.

Tags

CCSS.HSF.BF.A.2

Which formula represents the nth term of an arithmetic sequence?

• an = a1 + (n - 1)d

• an = a1 - (n + 1)d

• an = n² + a1

• an = a1⋅n + d

Answer explanation

The formula an = a1 + (n - 1)d correctly represents the nth term of an arithmetic sequence, where a1 is the first term and d is the common difference. The other options do not follow the arithmetic sequence definition.

Tags

CCSS.HSF.BF.A.2

In an arithmetic sequence where the first term is 10 and the 6th term is 34, what is the common difference?

• 6

• 8.2

• 10.4

• 4.8

Answer explanation

In an arithmetic sequence, the nth term is given by a_n = a_1 + (n-1)d. Here, a_1 = 10 and a_6 = 34. So, 34 = 10 + 5d. Solving for d gives d = (34 - 10) / 5 = 4.8. Thus, the common difference is 4.8.

Tags

CCSS.HSF.BF.A.2