Question

Write an equation for the following sequence: -3, 1, 5, 9, 13, ... Use a, = 04+ (n - 1)d Make sure you simplify all the way you can."

a) a = -3 + (n - 1)4
b) a = -3 + (n - 1)5
c) a = -3 + (n - 1)6
d) a = -3 + (n - 1)7

Answer 1

The correct equation for the given arithmetic sequence is a_n = -3 + (n - 1)4, which simplifies to a_n = 4n - 7. However, out of the provided options, option (a) reflects the correct unsimplified formula.

Step-by-step explanation:

The sequence in question begins with -3, and each subsequent term increases by 4. That means we have an arithmetic sequence with the first term (a) equal to -3 and a common difference (d) of 4. The general formula for the nth term of an arithmetic sequence is a_n = a + (n - 1)d. So, substituting a = -3 and d = 4, we simplify the equation as follows:

• a_n = -3 + (n - 1)4
• a_n = -3 + 4n - 4
• a_n = 4n - 7 (after combining like terms)

However, this final equation does not match any of the given options. The closest match is option (a), which is the same as our equation but does not include the final simplification step (combining -3 and -4 into -7).