Question

The first term of an arithmetic sequence is 23, and the 37th term of the sequence is -49. What is the common difference of the sequence?

A) -4
B) -3
C) -2
D) -1

Answer 1

The common difference of the arithmetic sequence is calculated using the formula for the nth term. By plugging in the known first term and the 37th term, the common difference is found to be -2.

Step-by-step explanation:

To find the common difference of an arithmetic sequence, we use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n-1)d

Where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference. We have the first term, a_1 = 23, and the 37th term, a_37 = -49.

Let's use this information:

-49 = 23 + (37-1)d

-49 = 23 + 36d

Now subtract 23 from both sides:

-49 - 23 = 36d

-72 = 36d

Divide both sides by 36 to find d:

d = -72 / 36

d = -2

So, the common difference of the sequence is -2, which corresponds to option C).