square root of (12), square root of (12 + square root of (12)), square root of (12+ square root of (12+ square root of (12)))
Write a recursion formaula for an(subcription), n greater than or equal to 2.
To write a recursion formula for an(subscription), where n is greater than or equal to 2, you can observe that each term is calculated by taking the square root of the previous term and adding it to the original number (12 in this case).
Let's break down the given sequence:
a1 = square root of (12)
a2 = square root of (12 + square root of (12))
a3 = square root of (12 + square root of (12 + square root of (12)))
To generalize this pattern, we can say that for any n greater than or equal to 2:
an = square root of (12 + an-1)
In this formula, an-1 represents the previous term in the sequence, and an represents the current term.
For example:
a2 = square root of (12 + a1)
a3 = square root of (12 + a2)
a4 = square root of (12 + a3)
and so on...
By using this recursion formula, you can find any term in the sequence by knowing the previous term(s).