Q. h(n)=−10+12nComplete the recursive formula of h(n). h(1)=□h(n)=h(n−1)+□
Determine first term: Determine the first term of the sequence h(n).To find h(1), we substitute n=1 into the formula h(n)=−10+12n.h(1)=−10+12(1)=−10+12=2
Find common difference: Find the difference between consecutive terms to identify the common difference.To find the common difference, we can calculate h(2)−h(1).h(2)=−10+12(2)=−10+24=14The common difference is h(2)−h(1)=14−2=12.
Write recursive formula: Write the recursive formula using the first term and the common difference.The recursive formula for an arithmetic sequence is h(n)=h(n−1)+d, where d is the common difference.Since we have found that h(1)=2 and the common difference d=12, the recursive formula is:h(n)=h(n−1)+12
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