Question

What kind of sequence is this? –58, 58, –174, 870, ...

Answer 1

To identify the type of sequence, let's examine the given numbers: –58, 58, –174, 870.

First, we can look at the differences between consecutive terms to see if it follows a specific pattern:

1. From –58 to 58:
\( 58 - (-58) = 58 + 58 = 116 \)

2. From 58 to –174:
\( -174 - 58 = -174 - 58 = -232 \)

3. From –174 to 870:
\( 870 - (-174) = 870 + 174 = 1044 \)

Now, we have the first differences:
- From first to second term: \( 116 \)
- From second to third term: \( -232 \)
- From third to fourth term: \( 1044 \)

Now, we can look at the ratio of consecutive terms to see if it reveals a multiplicative pattern:

1. \( \frac{58}{-58} = -1 \)
2. \( \frac{-174}{58} = -3 \)
3. \( \frac{870}{-174} = -5 \)

The ratios are:
- From the first term to the second: \( -1 \)
- From the second term to the third: \( -3 \)
- From the third term to the fourth: \( -5 \)

The pattern of multipliers seems to be an increasing odd number (like -1, -3, -5).

Although the specific type of sequence is not immediately clear, it appears to oscillate in sign and the numbers' values increase significantly with each step.

Thus, it does not align neatly with a simple arithmetic, geometric, or harmonic sequence. Given the pattern observed with the differences and ratios, it looks like a sequence based on a custom rule or polynomial relation, possibly quadratic in nature, but without a definitive formula from the terms provided.

Based on what we've gathered, it can be categorized as a nonlinear sequence with alternating signs and growing magnitudes.