Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n=1 for the first term. –8,–16,–32,…Write your answer using decimals and integers.an=____(____)n−1
Q. Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n=1 for the first term. –8,–16,–32,…Write your answer using decimals and integers.an=____(____)n−1
Identify sequence type: Identify the type of sequence.The sequence is −8, −16, −32, ...Each term is obtained by multiplying the previous term by a common ratio.Therefore, the sequence is geometric.
Determine first term and ratio: Determine the first term (a1) and the common ratio (r).The first term: a1=−8To find the common ratio, divide the second term by the first term: r=(−16)/(−8)=2
Write nth term formula: Write the formula for the nth term of a geometric sequence.The formula for the nth term an of a geometric sequence is an=a1⋅r(n−1).
Substitute values into formula: Substitute the values of a1 and r into the formula.a1=−8 and r=2 So, an=(−8)×2(n−1)
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