Answer:


b) 4998
c) explicit rule (see below for explanation)
d) see below
Step-by-step explanation:
An explicit formula for an <u>arithmetic sequence</u> allows you to find the nth term of the sequence.
A recursive formula for an <u>arithmetic sequence</u> allows you to find the nth term of the sequence <em>provided </em>you know the value of the previous term in the sequence.
<h3><u>
Part a</u></h3>
<u>Explicit Formula</u>

where:
is the nth term- a is the first term
- n is the number of the term
- d is the common difference
<u>Given sequence</u>: 3, 8, 13, 18, 23, ...
To find the <u>common difference</u>, subtract one term from the next term.
Therefore:
Substituting the found values of a and d into the formula to create a explicit rule for the given sequence:



<u>Recursive Formula</u>

where:
is the nth term
is the term immediately before the nth term- d is the common difference
We already know the common difference our previous calculations.
Therefore:

When giving a recursive rule we also have to define the <u>first term</u> of the sequence, as it is not part of the formula. Therefore, the full recursive rule for the given sequence is:

<h3><u>Part b</u></h3>
To find the 1000th term of the sequence, use the <u>explicit rule</u> and substitute n = 1000:



Therefore, the 1000th term of the sequence is 4998.
<h3><u>Part c</u></h3>
We used the explicit rule to find the 1000th term as this rule allows us to find the nth term of the sequence <em>without </em>having to know any previous terms.
<h3><u>Part d</u></h3>
The <u>disadvantage</u> of a recursive rule when compared to an explicit rule is that we need to know the <u>previous term</u> to find the nth term, whereas the explicit rule doesn't need this information.
Learn more about sequences here:
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