Write down the general term of each sequence. (a) 2, 3, 4, 5, ... (b) 38, 35, 32, 29, ...
Understand the Problem
The question is asking to identify and write down the general term for two given sequences. The first sequence starts from 2 and increments by 1, while the second sequence starts from 38 and decrements by 3.
Answer
The general terms for the sequences are $a_n = n + 1$ and $b_n = 41 - 3n$.
Answer for screen readers
The general terms for the sequences are:
(a) $a_n = n + 1$
(b) $b_n = 41 - 3n$
Steps to Solve
- Identify the pattern in the first sequence
The first sequence starts at 2 and increases by 1 each time. The terms are: 2, 3, 4, 5, ...
- Determine the formula for the first sequence
The nth term can be represented as: $$ a_n = 2 + (n - 1) \cdot 1 $$ This simplifies to: $$ a_n = n + 1 $$
- Identify the pattern in the second sequence
The second sequence starts at 38 and decreases by 3 each time. The terms are: 38, 35, 32, 29, ...
- Determine the formula for the second sequence
The nth term can be represented as: $$ b_n = 38 - (n - 1) \cdot 3 $$ This simplifies to: $$ b_n = 41 - 3n $$
The general terms for the sequences are:
(a) $a_n = n + 1$
(b) $b_n = 41 - 3n$
More Information
These general terms allow you to calculate any term in the sequence by substituting the term number (n) into the equations. For example, for the first sequence, if you wanted the 5th term, you would calculate $5 + 1 = 6$.
Tips
- Confusing the direction of the sequence (increasing vs. decreasing).
- Failing to notice the starting value when creating the formula.
- Miscalculating the term number when plugging into the formula.
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