Question

functions and lines
identifying arithmetic sequences and finding the common difference
for each sequence, determine whether it appears to be arithmetic.
if it does, find the common difference.
-8, -15, -22, -29, ...
arithmetic
common difference: d =
not arithmetic
-1, 2, 5, 8, ...
arithmetic
common difference: d =
not arithmetic
2, 20, 200, 2000, ...
arithmetic
common difference: d =
not arithmetic

Explanation:

Step1: Analyze first sequence

For the sequence \(-8, -15, -22, -29, \dots\), we check the difference between consecutive terms.
First difference: \(-15 - (-8) = -15 + 8 = -7\)
Second difference: \(-22 - (-15) = -22 + 15 = -7\)
Third difference: \(-29 - (-22) = -29 + 22 = -7\)
Since the differences are constant (\(-7\)), it is arithmetic with \(d = -7\).

Step2: Analyze second sequence

For the sequence \(-1, 2, 5, 8, \dots\), check consecutive differences.
First difference: \(2 - (-1) = 2 + 1 = 3\)
Second difference: \(5 - 2 = 3\)
Third difference: \(8 - 5 = 3\)
Differences are constant (\(3\)), so it is arithmetic with \(d = 3\).

Step3: Analyze third sequence

For the sequence \(2, 20, 200, 2000, \dots\), check differences.
First difference: \(20 - 2 = 18\)
Second difference: \(200 - 20 = 180\)
Third difference: \(2000 - 200 = 1800\)
Differences are not constant, so it is not arithmetic.

Answer:

1. For \(-8, -15, -22, -29, \dots\): Arithmetic, \(d = -7\)
2. For \(-1, 2, 5, 8, \dots\): Arithmetic, \(d = 3\)
3. For \(2, 20, 200, 2000, \dots\): Not arithmetic