write a recursive formula for 8,6,4,2,0 then find a14
To find a recursive formula for the given sequence (8, 6, 4, 2, 0), we need to identify the pattern or rule that describes how each term is related to the previous term(s).
Looking at the sequence, it seems that each term is obtained by subtracting 2 from the previous term. So, we can write a recursive formula using this relationship.
Let's denote the nth term as aₙ. From the second term onwards, each term is obtained by subtracting 2 from the previous term:
aₙ = aₙ₋₁ - 2
Where:
aₙ: nth term of the sequence
aₙ₋₁: (n-1)th term of the sequence
Now that we have the recursive formula, we can find a14 by substituting the values into the formula and recursively calculating the sequence until we reach the 14th term.
Starting with the given initial terms:
a₁ = 8
a₂ = a₁ - 2 = 6
a₃ = a₂ - 2 = 4
a₄ = a₃ - 2 = 2
a₅ = a₄ - 2 = 0
Continuing this pattern, we can find a14:
a₆ = a₅ - 2 = 0 - 2 = -2
a₇ = a₆ - 2 = -2 - 2 = -4
a₈ = a₇ - 2 = -4 - 2 = -6
...
By continuing this recursive process, we can find a14.