What is the third term of the sequence defined by the recursive rule f(1)=2, f(n)=2f(n-1)+1?
Please help.
n = 1
f(1) = 2
f(n) = 2 f(n-1) + 1
n = 2
f(2) = 2 f(2 - 1) + 1 = 2 f(1) + 1 = 2 ∙ 2 + 1 = 4 + 1 = 5
n = 3
f(3) = 2 f(3 - 1) + 1 = 2 f(2) + 1 = 2 ∙ 5 + 1 = 10 + 1 = 11
11
Ah, yes, the infamous recursive sequence. Let's crack a joke while we solve this: Why don't scientists trust atoms? Because they make up everything!
Now, let's get to it. We're given that f(1) = 2, and the recursive rule f(n) = 2f(n-1) + 1. We need to find the third term, which is f(3).
To find f(3), we can work our way up through the sequence:
f(2) = 2f(1) + 1 = 2(2) + 1 = 5
f(3) = 2f(2) + 1 = 2(5) + 1 = 11
So, the third term of the sequence is 11. Keep those math questions coming!
To find the third term of the sequence defined by the recursive rule f(1) = 2, f(n) = 2f(n-1) + 1, we need to apply the recursive rule twice.
The first term of the sequence is given as f(1) = 2.
To find the second term, we use the recursive formula f(n) = 2f(n-1) + 1. Plugging in n = 2, we have:
f(2) = 2f(2-1) + 1
f(2) = 2f(1) + 1
f(2) = 2 * 2 + 1
f(2) = 4 + 1
f(2) = 5
Now, to find the third term, we again use the recursive formula:
f(3) = 2f(3-1) + 1
f(3) = 2f(2) + 1
f(3) = 2 * 5 + 1
f(3) = 10 + 1
f(3) = 11
Therefore, the third term of the sequence is 11.