Help me with this 1,2,3. For each sequence, Determine with whether it appears to be arithmetic If it does find a common difference

Problem 1

Explanation:

Pick any term of the sequence, and subtract off the previous term to find that,

Each time we get the same result, so that means we have an arithmetic sequence with common difference -4

This indicates that adding -4 to each term, or subtracting 4 from each term, will generate the next one.

Eg: term2 = term1 - 4 = -8-4 = -12.

Problem 2

Explanation:

Similar to problem 1, this sequence is also arithmetic because we add on 5 to each term to get the next one

Or you could subtract adjacent terms as done in problem 1, to find that the common difference is 5.

Problem 3

Explanation:

Unlike the previous two problems, this sequence is not arithmetic.

We can see that

The gaps of 9 and 36 aren't the same. We need the same common difference between any adjacent terms to have an arithmetic sequence.

This sequence is instead geometric because

Each quotient is 4, showing the common ratio is 4. To find the next term, we multiply the current term by 4. So the next term after 192 would be 4*192 = 768, then 4*768 = 3072 is next, and so on.

step-by-step explanation: