Question

Find the common difference of an arithmetic sequence if the first term is 8 and the fourth term is -1.

a₄ = -1, n = 4

Find:

A. Common difference = -3
B. Common difference = -4
C. Common difference = -2
D. Common difference = -1

Given: a₁ = 8

Answer 1

The common difference of the arithmetic sequence is found using the formula for the nth term of an arithmetic sequence. By plugging the values of the first and fourth terms into the formula and solving for the common difference, the answer is determined to be -3.

Step-by-step explanation:

The question asks to find the common difference of an arithmetic sequence where the first term (a₁) is 8 and the fourth term (a₄) is -1. In an arithmetic sequence, the common difference (d) is the constant amount we add to each term to get the next term. Since we know the value of the first and fourth terms, we can use the formula a₄ = a₁ + (n - 1)d, where n is the term number, to find the common difference. Substituting the known values, we have:

-1 = 8 + (4 - 1)d

-1 = 8 + 3d

-9 = 3d

d = -3

Therefore, the common difference of the arithmetic sequence is -3.