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h(n)=10+12nh(n)=-10+12n\newlineComplete the recursive formula of h(n)h(n). \newline h(1)=h(1)=\square \newline h(n)=h(n1)+h(n)=h(n-1)+\square

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Q. h(n)=10+12nh(n)=-10+12n\newlineComplete the recursive formula of h(n)h(n). \newline h(1)=h(1)=\square \newline h(n)=h(n1)+h(n)=h(n-1)+\square
  1. Determine first term: Determine the first term of the sequence h(n)h(n).\newlineTo find h(1)h(1), we substitute n=1n = 1 into the formula h(n)=10+12nh(n) = -10 + 12n.\newlineh(1)=10+12(1)=10+12=2h(1) = -10 + 12(1) = -10 + 12 = 2
  2. Find common difference: Find the difference between consecutive terms to identify the common difference.\newlineTo find the common difference, we can calculate h(2)h(1)h(2) - h(1).\newlineh(2)=10+12(2)=10+24=14h(2) = -10 + 12(2) = -10 + 24 = 14\newlineThe common difference is h(2)h(1)=142=12h(2) - h(1) = 14 - 2 = 12.
  3. Write recursive formula: Write the recursive formula using the first term and the common difference.\newlineThe recursive formula for an arithmetic sequence is h(n)=h(n1)+dh(n) = h(n-1) + d, where dd is the common difference.\newlineSince we have found that h(1)=2h(1) = 2 and the common difference d=12d = 12, the recursive formula is:\newlineh(n)=h(n1)+12h(n) = h(n-1) + 12

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