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Complete the recursive formula of the arithmetic sequence 9,-1,-11,-21,dots d(1)= d(n)=d(n-1)+

Complete the recursive formula of the arithmetic sequence 9,−1,−11,−21,… 9,-1,-11,-21, \ldots .\newlined(1)= d(1)= \newlined(n)=d(n−1)+ d(n)=d(n-1)+

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Q. Complete the recursive formula of the arithmetic sequence 9,−1,−11,−21,… 9,-1,-11,-21, \ldots .\newlined(1)= d(1)= \newlined(n)=d(n−1)+ d(n)=d(n-1)+
  1. Determining the Common Difference: To find the recursive formula for the arithmetic sequence, we need to determine the common difference between consecutive terms. We can do this by subtracting any term from the term that follows it.\newlineCalculation: \newline−1−9=−10-1 - 9 = -10\newline−11−(−1)=−10-11 - (-1) = -10\newline−21−(−11)=−10-21 - (-11) = -10\newlineThe common difference dd is −10-10.
  2. Writing the Recursive Formula: Now that we have the common difference, we can write the recursive formula. The first term of the sequence, d(1)d(1), is given as 99. The recursive formula will express each term as the previous term plus the common difference.\newlineThe recursive formula is:\newlined(1)=9d(1) = 9\newlined(n)=d(n−1)+(−10)d(n) = d(n-1) + (-10) for n > 1

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