Question

In an arithmetic sequence, the first term, a₁, is equal to 8, and the sixth term, a₆, is equal to 58. Which number represents the common difference of the arithmetic sequence?

Answer 1

The common difference of the arithmetic sequence is 10, calculated by using the formula for the nth term of an arithmetic sequence with the given first and sixth terms.

Step-by-step explanation:

To find the common difference in the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the term number. Given the first term a1 = 8 and the sixth term a6 = 58, we can substitute these values into the formula to get 58 = 8 + (6 - 1)d.

Solving for d, we get d = (58 - 8) / (6 - 1) = 50 / 5 = 10. Therefore, the common difference of the arithmetic sequence is 10.