Solution:
We can see that each term when subtracted by 4, gives the next term.
This means that:
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)".
