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Answer:
Recursive:
Explicit:
And the 20th term is 225.
Step-by-step explanation:
We have the sequence:
35, 45, 55, 65.
Notice that each subsequent term is 10 more than the previous term.
Therefore, our common difference is (+)10.
Recursive Rule:
The standard format for the recursive rule is:
Where a is the initial term and d is the common difference.
From our sequence, we know that a the initial term is 35.
And as determined, our common difference d is 10.
Substitute. Hence, our recursive rule is:
Explicit Rule:
The standard format for the explicit rule is:
Where a is the initial term and d is the common difference. So, let’s substitute 35 for a and 10 for d. Hence, our explicit formula is:
Now, let’s find the 20th term. We will utilize the explicit rule since the recursive rule can get tedious. Substitute 20 for n because we would like to 20th term. Thus:
Evaluate:
Hence, the 20th term is 225.