Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n=1 for the first term.–31,–30,–29,–28,…an=_____
Q. Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n=1 for the first term.–31,–30,–29,–28,…an=_____
Identify type of sequence: Identify the type of sequence.The sequence is −31, −30, −29, −28, .... We need to determine if this sequence is arithmetic or geometric. By looking at the sequence, we can see that there is a constant difference between consecutive terms, which means the sequence is arithmetic.
Find first term and difference: Find the first term and the common difference.The first term of the sequence, a1, is –31. To find the common difference, d, we subtract the first term from the second term: d=(–30)–(–31)=–30+31=1.
Write formula for nth term: Write the formula for the nth term of an arithmetic sequence. The general formula for the nth term of an arithmetic sequence is an=a1+(n−1)d. We have a1=−31 and d=1.
Substitute values into formula: Substitute the values of a1 and d into the formula.Substituting the values into the formula gives us an=(−31)+(n−1)(1).
Simplify the expression: Simplify the expression.Simplifying the expression, we get an=−31+n−1. Combining like terms, we get an=n−32.
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