Question

Determine whether the sequences given below form arithmetic progressions, and the next three numbers in the sequence. Then identify the common difference. 4,0,-4,-8,-12,

Answer 1

The sequence 4, 0, -4, -8, -12 is an arithmetic progression with a common difference of -4. The next three numbers are -16, -20, and -24.

Step-by-step explanation:

To determine whether the sequence 4, 0, -4, -8, -12 forms an arithmetic progression, we need to check if the difference between consecutive terms is constant. Subtracting each term from the one before it, we get:
0 - 4 = -4,
-4 - 0 = -4,
-8 - (-4) = -4,
-12 - (-8) = -4.

Since the difference is the same for each pair of consecutive terms, the sequence is indeed an arithmetic progression with a common difference of -4. The next three numbers in the sequence would be found by subtracting 4 from the last given number successively:
-12 - 4 = -16,
-16 - 4 = -20,
-20 - 4 = -24.

Therefore, the next three numbers in the sequence are -16, -20, and -24.