Answer :
An arithmetic sequence is defined by a constant difference between consecutive terms. We are given the sequence:
[tex]$$
14,\,24,\,34,\,44,\,54,\,\ldots
$$[/tex]
Step 1. Identify the first term.
The first term is given by
[tex]$$
f(1) = 14.
$$[/tex]
Step 2. Calculate the common difference.
To find the common difference, subtract the first term from the second term:
[tex]$$
24 - 14 = 10.
$$[/tex]
So, the common difference is [tex]$10$[/tex].
Step 3. Write the recursive function.
An arithmetic sequence has the recursive form:
[tex]$$
f(n+1) = f(n) + \text{(common difference)}.
$$[/tex]
Substitute the known values:
[tex]$$
f(n+1) = f(n) + 10, \quad \text{where } f(1) = 14.
$$[/tex]
Step 4. Identify the correct statement.
Among the statements provided, the one that matches our recursive function is:
- The common difference is 10, so the function is [tex]$f(n+1)=f(n)+10$[/tex] where [tex]$f(1)=14$[/tex].
Thus, the correct answer is the statement numbered 3.
[tex]$$
14,\,24,\,34,\,44,\,54,\,\ldots
$$[/tex]
Step 1. Identify the first term.
The first term is given by
[tex]$$
f(1) = 14.
$$[/tex]
Step 2. Calculate the common difference.
To find the common difference, subtract the first term from the second term:
[tex]$$
24 - 14 = 10.
$$[/tex]
So, the common difference is [tex]$10$[/tex].
Step 3. Write the recursive function.
An arithmetic sequence has the recursive form:
[tex]$$
f(n+1) = f(n) + \text{(common difference)}.
$$[/tex]
Substitute the known values:
[tex]$$
f(n+1) = f(n) + 10, \quad \text{where } f(1) = 14.
$$[/tex]
Step 4. Identify the correct statement.
Among the statements provided, the one that matches our recursive function is:
- The common difference is 10, so the function is [tex]$f(n+1)=f(n)+10$[/tex] where [tex]$f(1)=14$[/tex].
Thus, the correct answer is the statement numbered 3.
