What is the pattern in the sequence 100, 19, 83, 34, 70, 45?

Answer 1

#a_0 = 100#
#a_n = a_(n-1) + (-1)^n*(10-n)^2#

or

#a_(2n) = 100-19n+2n^2#
#a_(2n+1) = 19+17n-2n^2#

(See image below. I couldn't figure out an easy way to show this with standard text)

If you look at differences of alternate terms, you can find the formula for term n as follows:

#100, 83, 70 -> -17, -13 -> 4#

Hence #a_(2n) = 100 -17n +4(n(n-1))/(2!) = 100-19n+2n^2#

#19, 34, 45 -> 15, 11 -> -4#

Hence #a_(2n+1) = 19 +15n -4(n(n-1))/(2!) = 19+17n-2n^2#

See: https://tutor.hix.ai

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Answer 2

The pattern in the given sequence is as follows:

  1. Subtract 81 from the first number (100) to get the second number (19).
  2. Add 64 to the second number (19) to get the third number (83).
  3. Subtract 49 from the third number (83) to get the fourth number (34).
  4. Add 36 to the fourth number (34) to get the fifth number (70).
  5. Subtract 25 from the fifth number (70) to get the sixth number (45).

So, the pattern alternates between adding and subtracting consecutive perfect squares: (81, 64, 49, 36, 25).

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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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