Write a recursive formula for the arithmetic sequence {a_n}={2,7/2,5,13/2}

Answer 1

To find the recursive formula for an arithmetic sequence, we need to identify the common difference between consecutive terms. In this case, we can observe that the common difference between any two consecutive terms is 5/2.

Let's denote the first term of the sequence as a₁ = 2.

Now, let's express the n-th term, aₙ, in terms of aₙ₋₁:

aₙ₋₁ + (5/2) = aₙ

For n = 2, we have:

a₁ + (5/2) = a₂
2 + (5/2) = 7/2

For n = 3, we have:

a₂ + (5/2) = a₃
(7/2) + (5/2) = 12/2 + 5/2 = 17/2 = 8.5

For n = 4, we have:

a₃ + (5/2) = a₄
(8.5) + (5/2) = 17/2 + 10/2 = 27/2 = 13.5

Therefore, the recursive formula for the arithmetic sequence {aₙ} = {2, 7/2, 5, 13/2} is:

aₙ = aₙ₋₁ + (5/2)