What is the term-to-term rule of the following sequence?
3, 7, 11, 15, ...
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What is the term-to-term rule of the following sequence?
3, 7, 11, 15, ...
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Identify the common difference.
By examining the sequence: , we find that the difference () between each pair of consecutive terms is , , and . Hence, the common difference is 4.
Step 2: Use the arithmetic sequence formula.
The first term is 3. Using the formula for the nth term of an arithmetic sequence:
Substitute and :
Simplify this equation:
Step 3: Compare the rule with the provided choices.
The derived formula is which matches the choice .
Therefore, the term-to-term rule of the sequence is .
Is there a term-to-term rule for the sequence below?
18 , 22 , 26 , 30
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