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.-68,-136,-204,-272,…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.-68,-136,-204,-272,…an=_____
Identify sequence type: Identify the type of sequence.We have: –68,–136,–204,–272,…Is the given sequence geometric or arithmetic? Since there is a common difference between consecutive terms, the given sequence is arithmetic.
Find first term and difference: Determine the first term (a1) and the common difference (d) of the sequence.The first term, a1=−68Common difference, d=−136−(−68)=−68
Write nth term formula: Write the formula for the nth term of an arithmetic sequence. an=a1+(n−1)d
Substitute values into formula: Substitute the values of a1 and d into the formula.a1=−68d=−68an=−68+(n−1)(−68)
Simplify expression: Simplify the expression.an=−68−68(n−1)an=−68−68n+68an=−68n
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