Q: What is the formula for the following arithmetic sequence?

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We don't see a question like that very often at all. You've said "the following ..." twice in your question. "The following ... " means "I'm about to show you the item". In your question, there are supposed to be both a list of choices AND an arithmetic sequence "following" the question, but neither one is there. We don't stand a chance!

The following formula generalizes this pattern and can be used to find ANY term in an arithmetic sequence. a'n = a'1+ (n-1)d.

The sequence is neither arithmetic nor geometric.

yes it is

origin of arithmetic sequence

an = a1 + d(n - 1)

It is an arithmetic sequence for which the index goes on and on (and on).

An arithmetic sequence is a list of numbers which follow a rule. A series is the sum of a sequence of numbers.

-7

The 90th term of the arithmetic sequence is 461

Arithmetic

It is the start of an arithmetic sequence.

It appears to be -6

None, since there is nothing to link y to the sequence.

That's an arithmetic sequence.

You didn't say the series (I prefer to use the word sequence) of even numbers are consecutive even numbers, or even more generally an arithmetic sequence. If we are not given any information about the sequence other than that each member happens to be even, there is no formula for that other than the fact that you can factor out the 2 from each member and add up the halves, then multiply by 2: 2a + 2b + 2c = 2(a + b + c). If the even numbers are an arithmetic sequence, you can use the formula for the sum of an arithmetic sequence. Similarly if they are a geometric sequence.

It is an arithmetic sequence if you can establish that the difference between any term in the sequence and the one before it has a constant value.

Any pair of numbers will always form an arithmetic sequence.

The sequence in the question is NOT an arithmetic sequence. In an arithmetic sequence the difference between each term and its predecessor (the term immediately before) is a constant - including the sign. It is not enough for the difference between two successive terms (in any order) to remain constant. In the above sequence, the difference is -7 for the first two intervals and then changes to +7.

The answer depends on what the explicit rule is!

A single number, such as 13579, does not define a sequence.

No.

Since there is only one number, there is no sensible answer.

18 - 6n

No, the Fibonacci sequence is not an arithmetic because the difference between consecutive terms is not constant

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