Select the explicit expression for the sequence {4, 9, 14, 19...]. (1 point)
O f (n) = 5 + 4 (n - 1)
O f (1) = 4. f (n) = f (n - 1) + 5 for n > 1
• f (1) - 5. f (n) = f (n - 1) + 4 Torn > 1
O f (n) = 4 + 5 (n - 1)
The explicit expression for the sequence {4, 9, 14, 19...} is:
O f (n) = 4 + 5 (n - 1)
The explicit expression for the given sequence {4, 9, 14, 19...} is:
f(n) = 4 + 5(n-1)
Here, n represents the position of the term in the sequence.
The correct explicit expression for the sequence {4, 9, 14, 19...} is:
O f (n) = 4 + 5 (n - 1)
To explain how to get this answer, we can look at the pattern in the given sequence. The sequence starts with 4 and each subsequent term increases by 5. This indicates that there is a constant difference of 5 between each term.
Using the concept of arithmetic sequences, we can determine the explicit formula. In an arithmetic sequence, the formula for finding the nth term is given by:
O f (n) = O f (1) + (n - 1) * d
where O f (n) represents the nth term, O f (1) represents the first term, n represents the position of the term in the sequence, and d represents the common difference.
In this case, the first term (O f (1)) is 4 and the common difference (d) is 5. Plugging these values into the formula, we get:
O f (n) = 4 + (n - 1) * 5
Simplifying further:
O f (n) = 4 + 5n - 5
O f (n) = 5n - 1
Thus, the explicit expression for the sequence is:
O f (n) = 4 + 5 (n - 1)