Question
What kind of sequence is this?
–242, –224, –205, –185, ...
–242, –224, –205, –185, ...
Answers
Answered by
GPT-4o mini
The sequence provided is:
–242, –224, –205, –185, ...
To determine the type of sequence, we can examine the differences between consecutive terms:
- The difference between –224 and –242 is:
\(-224 - (-242) = –224 + 242 = 18\)
- The difference between –205 and –224 is:
\(-205 - (-224) = –205 + 224 = 19\)
- The difference between –185 and –205 is:
\(-185 - (-205) = –185 + 205 = 20\)
Now let's summarize the differences:
- First difference: 18
- Second difference: 19
- Third difference: 20
We can see that the sequence of differences is increasing by 1 each time, indicating that this is a quadratic sequence. In a quadratic sequence, the second differences (the differences of the first differences) are constant. Since our first differences are not constant but are increasing linearly, this indicates that the terms of the sequence can be modeled by a quadratic function.
To summarize, the sequence given is a quadratic sequence.
–242, –224, –205, –185, ...
To determine the type of sequence, we can examine the differences between consecutive terms:
- The difference between –224 and –242 is:
\(-224 - (-242) = –224 + 242 = 18\)
- The difference between –205 and –224 is:
\(-205 - (-224) = –205 + 224 = 19\)
- The difference between –185 and –205 is:
\(-185 - (-205) = –185 + 205 = 20\)
Now let's summarize the differences:
- First difference: 18
- Second difference: 19
- Third difference: 20
We can see that the sequence of differences is increasing by 1 each time, indicating that this is a quadratic sequence. In a quadratic sequence, the second differences (the differences of the first differences) are constant. Since our first differences are not constant but are increasing linearly, this indicates that the terms of the sequence can be modeled by a quadratic function.
To summarize, the sequence given is a quadratic sequence.