Which of the following is a proportional relationship? SELECT ALL THAT APPLY
2 answers:
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Answer:
Infinite series equals 4/5
Step-by-step explanation:
Notice that the series can be written as a combination of two geometric series, that can be found independently:
The first one: is a geometric sequence of first term (
) "1" and common ratio (r) "
", so since the common ratio is smaller than one, we can find an answer for the infinite addition of its terms, given by:
The second one: is a geometric sequence of first term "1", and common ratio (r) "
". Again, since the common ratio is smaller than one, we can find its infinite sum:
now we simply combine the results making sure we do the indicated difference: Infinite total sum=
Answer:
The given sequence 6, 7, 13, 20, ... is a recursive sequence
Step-by-step explanation:
As the given sequence is
- It cannot be an arithmetic sequence as the common difference between two consecutive terms in not constant.
As
,
As d is not same. Hence, it cannot be an arithmetic sequence.
- It also cannot be a geometrical sequence and exponential sequence.
It cannot be geometric sequence as the common ratio between two consecutive terms in not constant.
As
,
,
As r is not same, Hence, it cannot be a geometric sequence or exponential sequence. As exponential sequence and geometric sequence are basically the same thing.
So, if we carefully observe, we can determine that:
- The given sequence 6, 7, 13, 20, ... is a recursive sequence.
Please have a close look that each term is being created by adding the preceding two terms.
For example, the sequence is generated by starting from 1.
and
for n > 1.
<em>Keywords: sequence, arithmetic sequence, geometric sequence, exponential sequence</em>
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