What is the common difference between the first term of a linear sequence is 3 and the 8th term is 31?

The common difference in this linear sequence is 4.

Understanding Linear Sequences

A linear sequence, also known as an arithmetic sequence, is a sequence where the difference between consecutive terms remains constant. This constant difference is called the common difference.

To find the common difference, we can use the formula for the nth term of an arithmetic sequence:

a_n = a₁ + (n-1)d

Where:

• a_n is the nth term
• a₁ is the first term
• n is the term number
• d is the common difference

Calculating the Common Difference

In this problem:

• a₁ = 3 (first term)
• a₈ = 31 (8th term)
• n = 8

Substituting these values into the formula:

31 = 3 + (8-1)d

Solving for d:

31 = 3 + 7d
28 = 7d
d = 4

Therefore, the common difference is 4. This aligns with the information provided in multiple sources, including Quora and various other online resources. Each reference independently confirms the calculation and solution.