Question

Write an equation for the nth term of the arithmetic sequence. Then find a10.

a) a_n = -3n - 3, a10 = -33
b) a_n = -3n, a10 = -30
c) a_n = -3n - 2, a10 = -32
d) a_n = -3n - 1, a10 = -31

Answer 1

The correct equation for the nth term of the arithmetic sequence is a_n = -3n - 3, and the tenth term, a10, is -33.

Step-by-step explanation:

To find the equation for the nth term of an arithmetic sequence and then find a10, we must look at the formula given for a_n. The formula for an arithmetic sequence can be written as a_n = d(n - 1) + a_1 where d is the common difference and a_1 is the first term. Looking at the options provided, we have:

• a) a_n = -3n - 3, to find a10, we substitute n with 10: a10 = -3(10) - 3 = -30 - 3 = -33.
• b) a_n = -3n, to find a10: a10 = -3(10) = -30.
• c) a_n = -3n - 2, to find a10: a10 = -3(10) - 2 = -30 - 2 = -32.
• d) a_n = -3n - 1, to find a10: a10 = -3(10) - 1 = -30 - 1 = -31.

Matching the results with the options provided, we find that option a) is correct: the equation for the nth term is a_n = -3n - 3, and a10 is -33.