Q. Find an explicit formula for the arithmetic sequence10,−10,−30,−50,….Note: the first term should be c(1).c(n)=□
Determine Common Difference: To find an explicit formula for the arithmetic sequence, we first need to determine the common difference d between the terms. We can do this by subtracting any term from the term that follows it.Subtract the first term from the second term: −10−10=−20.
Write Explicit Formula: Now that we have the common difference, we can write the explicit formula for the arithmetic sequence. The general form of an arithmetic sequence is c(n)=c(1)+(n−1)d, where c(1) is the first term and d is the common difference.Since the first term c(1) is 10 and the common difference d is −20, we can substitute these values into the formula.c(n)=10+(n−1)(−20)
Simplify Formula: Simplify the formula by distributing the common difference −20 through the parentheses.c(n)=10−20(n−1)c(n)=10−20n+20
Combine Like Terms: Combine like terms to get the final explicit formula for the arithmetic sequence.c(n)=30−20n