Final answer:
To find the 31st term (a31) in the arithmetic sequence, we use the formula for the nth term. The formula involves the first term (-16) and the common difference (4), resulting in the 31st term being 104.
Step-by-step explanation:
To find the 31st term (a31) in the sequence -16, -12, -8, -4, we first determine the common difference and then apply the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where a1 is the first term and d is the common difference.
The common difference d can be found by subtracting any term from the following term. For example, -12 - (-16) = 4.
So, we have:
- First term (a1): -16
- Common difference (d): 4
- Term number (n): 31
Applying the arithmetic sequence formula:
a31 = -16 + (31 - 1)× 4
a31 = -16 + 30× 4
a31 = -16 + 120
a31 = 104
Therefore, the 31st term in the sequence is 104.