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37 POINTS PLEASE HELPPPPP!!!!!!

37 POINTS PLEASE HELPPPPP!!!!!!-example-1

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Solution:

We can see that each term when subtracted by 4, gives the next term.

This means that:

  • n₁ - 4(2) + 4(1) = n₂

Let's substitute the values to check:

  • => n₁ - 4(2) + 4(1) = n₂
  • => n₁ - 8 + 4 = n₂
  • => n₁ - 4 = n₂
  • => 18 - 4 = 14
  • => 14 = 14 (Proved)

Now, we can find the nth term aₙ by using the formula:

  • 18 - 4(nth term) + 4(1) = Value of nth term

To check that the formula is correct, let's substitute the value of nth as the fifth term of the sequence.

  • 18 - 4(nth term) + 4(1) = Value of nth term
  • => 18 - 4(5) + 4(1) = Value of 5th term
  • => 18 - 4(5) + 4(1) = Value of 5th term
  • => 18 - 20 + 4 = Value of 5th term
  • => 18 - 16 = Value of 5th term
  • => 2 = Value of 5th term

Now, let's find the fifth term mentally. Keep subtracting 4 until you reach the fifth term.

  • => 18 - 4 = Second term of sequence
  • => 14 = Second term of sequence
  • => 14 - 4 = Third term of sequence
  • => 10 = Third term of sequence
  • => 10 - 4 = Fourth term of sequence
  • => 6 = Fourth term of sequence
  • => 6 - 4 = Fifth term of sequence
  • => 2 = Fifth term of sequence

We are getting the same result from both ways.

In conclusion, our formula to find the nth term is "18 - 4(nth term) + 4(1)".

User LoneSpawn
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