Type of sequence: arithmetic progression
Explicit formula: 5n
Recursive formula: [tex]5_{n-1}[/tex] + 5
What does the word Sequence mean ?
A Sequence is a series of numbers in a regular pattern of increment. A sequence can be arithmetic or geometric in nature.
Given that a total value of a collection of nickels can be described by this sequence: 5, 10, 15, 20, 25, 30, .....
The difference in the sequence above is 10 - 5 = 5. There is an increment of 5 in each term.
Therefore, the type of sequence is arithmetic progression
The difference d = 5 and the first term is also 5
An explicit formula will be
a + (n - 1)d
substitute a and d into the formula
5 + (n - 1)5
5 + 5n - 5
5n
Therefore, 5n gives the value of a specific term based on the position
A recursive formula will be
[tex]a_{n-1}[/tex] + d
substitute a and d into the formula
[tex]5_{n-1}[/tex] + 5
Therefore, [tex]5_{n-1}[/tex] + 5 gives the value of a specific term based on the previous term
Learn more about Sequence here: https://brainly.com/question/6561461
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