Question

For the given explicit rule of an arithmetic sequence, an = -4 + (n - 1)7:

a) What is the common difference (d) of the arithmetic sequence?
b) What is the first term of the arithmetic sequence?
c) Fill in the values of x, y, and z to complete the table for the arithmetic sequence.

Answer 1

The common difference of the arithmetic sequence is 7. The first term of the arithmetic sequence is -4. The table values are filled in using the explicit rule.

Step-by-step explanation:

a) The common difference (d) of an arithmetic sequence is the constant value added to each term to get the next term. In this case, the common difference is 7, as shown by the equation an = -4 + (n - 1)7.

b) The first term of an arithmetic sequence can be found by substituting n = 1 into the given explicit rule. In this case, the first term is a1 = -4 + (1 - 1)7 = -4 + 0 = -4.

c) To fill in the table for the arithmetic sequence, we can start by substituting the values of n into the explicit rule and calculating the corresponding terms.