Q. Find an explicit formula for the arithmetic sequence10,−10,−30,−50,….. Note: the first term should be c(1).c(n)=□
Identify sequence type: Identify whether the given sequence is geometric or arithmetic. The sequence 10,−10,−30,−50,… has a common difference between consecutive terms, so it is an arithmetic sequence.
Determine first term and common difference: Determine the first term c(1) and the common difference d of the sequence. The first term c(1) is 10. To find the common difference, subtract the second term from the first term: d=−10−10=−20.
Use explicit formula for arithmetic sequence: Use the explicit formula for an arithmetic sequence, c(n)=c(1)+(n−1)d, where c(1) is the first term and d is the common difference. For this sequence, c(1)=10 and d=−20.
Write expression for the sequence: Substitute the values of c(1) and d into the formula to write an expression to describe the sequence. The expression for the sequence is c(n)=10+(n−1)(−20).
Simplify the expression: Simplify the expression. c(n)=10−20(n−1)=10−20n+20=30−20n.
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