Select the explicit expression for the sequence {4, 9, 14, 19...}. (1 point)
Responses
f(1)=5, f(n)=f(n−1)+4 for n>1
f left parenthesis 1 right parenthesis equals 5 , f left parenthesis n equals f left parenthesis n minus 1 right parenthesis plus 4 for n greater than 1
f(1)=4, f(n)=f(n−1)+5 for n>1
f left parenthesis 1 right parenthesis equals 4 , f left parenthesis n equals f left parenthesis n minus 1 right parenthesis plus 5 for n greater than 1
f(n)=5+4(n−1)
f left parenthesis n equals 5 plus 4 times left parenthesis n minus 1 right parenthesis
f(n)=4+5(n−1)
f left parenthesis n equals 4 plus 5 times left parenthesis n minus 1 right parenthesis
The explicit expression for the sequence {4, 9, 14, 19...} is f(n)=4+5(n−1).
To find the explicit expression for the sequence {4, 9, 14, 19...}, we need to observe the pattern in the sequence.
Looking at the sequence, we can see that each term is obtained by adding 5 to the previous term. So, the explicit expression for this sequence would be of the form f(n) = f(n-1) + 5, where f(n) represents the nth term in the sequence.
Now, let's consider the given options and determine the correct choice:
1. f(1) = 5, f(n) = f(n-1) + 4 for n > 1: This option does not match the pattern we observed in the sequence. The difference between consecutive terms is 5, not 4. Therefore, this option is incorrect.
2. f(1) = 4, f(n) = f(n-1) + 5 for n > 1: This option matches the pattern we observed. The first term is 4, and each subsequent term is obtained by adding 5 to the previous term. Therefore, this option is the correct explicit expression for the given sequence.
3. f(n) = 5 + 4(n-1): This option does not match the pattern in the sequence. The difference between consecutive terms is 5, not 4. Therefore, this option is incorrect.
4. f(n) = 4 + 5(n-1): This option does not match the pattern in the sequence. The difference between consecutive terms is 5, not 4. Therefore, this option is incorrect.
Therefore, the correct explicit expression for the sequence {4, 9, 14, 19...} is f(1) = 4, f(n) = f(n-1) + 5 for n > 1.