About Introduction to Sequences:
In this section, we learned the basic definition of a sequence. A sequence is a function that computes an ordered list of numbers. Our goal is to be able to find the first few terms of a sequence. If the sequence is defined explicitly, then we simply use the first few natural numbers to plug in for "n" and simplify. If the sequence is defined recursively, then we need to think about how the previous term(s) interact with the formula before plugging in for "n".
Test Objectives
- Demonstrate the ability to find the first few terms of a sequence defined by an explicit formula
- Demonstrate the ability to find the first few terms of a sequence defined by a recursive formula
#1:
Instructions: Find the first five terms of the sequence.
$$a)\hspace{.2em}a_n=-11 + 20n$$
$$b)\hspace{.2em}a_n=-74 + 100n$$
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#2:
Instructions: Find the first five terms of the sequence.
$$a)\hspace{.2em}a_n=-224 + 200n$$
$$b)\hspace{.2em}a_n=-16 + 6n$$
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#3:
Instructions: Find the first five terms of the sequence.
$$a)\hspace{.2em}a_n=30n$$
$$b)\hspace{.2em}a_{n + 1}=a_n - 200$$ $$a_1=18$$
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#4:
Instructions: Find the first five terms of the sequence.
$$a)\hspace{.2em}a_{n + 1}=a_n - 100$$ $$a_1=20$$
$$b)\hspace{.2em}a_{n + 1}=a_n - 100$$ $$a_1=37$$
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#5:
Instructions: Find the first five terms of the sequence.
$$a)\hspace{.2em}a_{n + 1}=a_n - 6$$ $$a_1=38$$
$$b)\hspace{.2em}a_{n + 1}=a_n - 5$$ $$a_1=-1$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}9, 29, 49, 69, 89$$
$$b)\hspace{.2em}26, 126, 226, 326, 426$$
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#2:
Solutions:
$$a)\hspace{.2em}{-}24, 176, 376, 576, 776$$
$$b)\hspace{.2em}{-}10, -4, 2, 8, 14$$
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#3:
Solutions:
$$a)\hspace{.2em}30, 60, 90, 120, 150$$
$$b)\hspace{.2em}18, -182, -382, -582, -782$$
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#4:
Solutions:
$$a)\hspace{.2em}20, -80, -180, -280, -380$$
$$b)\hspace{.2em}37, -63, -163, -263, -363$$
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#5:
Solutions:
$$a)\hspace{.2em}38, 32, 26, 20, 14$$
$$b)\hspace{.2em}{-}1, -6, -11, -16, -21$$
