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Write an expression to describe the sequence below. Use to represent the position of a term in the sequence, where for the first term._____
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Q. Write an expression to describe the sequence below. Use to represent the position of a term in the sequence, where for the first term._____
- Determine Sequence Type: We have the sequence: First, we need to determine if the sequence is arithmetic or geometric. By observing the sequence, we can see that there is a constant difference between consecutive terms, which indicates that the sequence is arithmetic.
- Identify First Term and Difference: Next, we need to identify the first term of the sequence, , and the common difference, . The first term, , is . To find the common difference, we subtract the first term from the second term: .
- Write General Formula: Now, we can write the general formula for the nth term of an arithmetic sequence, which is: .Substituting the values of and into the formula, we get: .
- Simplify Expression: Simplifying the expression, we have: .Combining like terms, we get: .This is the expression that describes the given sequence.
