What is the formula for the sequence #2, -1, 4, -7, 10, -13, 16,...# ?

Answer 1

The given sequence is matched by the formula:

#a_n = (-1)^n (-2+3(n-1))#

or if you prefer:

#a_n = (-1)^n (3n-5)#

No infinite sequence is determined purely by a finite number of terms, unless you are given further information - e.g. that the sequence is arithmetic or geometric.

That having been said, note that if we multiply the terms of the given sequence by #(-1)^n#, then we get the sequence:
#-2, 1, 4, 7, 10, 13, 16,...#
which is (as far as it goes) an arithmetic sequence with initial term #-2# and common difference #3#.

So a formula that fits the original sequence can be written:

#a_n = (-1)^n (-2+3(n-1))#
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Answer 2

The formula for the given sequence is (a_n = (-1)^{n+1}(3n - 1)), where (n) is the position of the term in the sequence starting from (n = 1).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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