Select the recursive formula for the sequence {2, 12, 22,
32...}. (1 point)
© f (n.) = 10 + 2 (n - 1)
O f (1) = 10. / (n) = / (n. - 1) + 2 for. n. 7
1
O f (n) = 2 + 10 (n
The correct recursive formula for the sequence {2, 12, 22, 32...} is:
f(n) = f(n-1) + 10
The correct recursive formula for the sequence {2, 12, 22, 32...} is f (n) = f (n-1) + 10, with f (1) = 2.
To determine the recursive formula for the sequence {2, 12, 22, 32...}, we need to identify the pattern in the sequence. Looking at the progression, we can see that each term increases by 10.
Given that the first term is 2, we can use this information to find the recursive formula. Let's break down the steps:
Step 1: Determine the formula for the general term.
The general term in this sequence can be represented as an + b, where a is the common difference (10 in this case), and b is the first term (2 in this case). Hence, the general term formula is an + b.
Step 2: Write the formula in terms of the term number (n).
Replace n with the term number in the general term formula. In this case, we use f(n) to represent the nth term. So, the formula becomes f(n) = 10n + 2.
Step 3: Express the recursive relationship.
In a recursive formula, the value of a term is defined in terms of the previous term(s). Let's assume that f(1) = 10, which means the first term is 10. Now, let's express the nth term in terms of the previous term:
f(n) = f(n-1) + 10
This recursive formula states that to find the nth term, we take the previous term (n-1) and add 10 to it.
So, after following the steps, the correct recursive formula for the sequence {2, 12, 22, 32...} is:
f(n) = f(n-1) + 10