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{[h(1)=-5.3],[h(n)=h(n-1)*(-11)]:} Find an explicit formula for h(n). h(n)=

{h(1)=−5.3,h(n)=h(n−1)⋅(−11)\begin{cases} h(1)=-5.3, h(n)=h(n-1)\cdot(-11) \end{cases} Find an explicit formula for h(n)h(n). h(n)=h(n)=

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Q. {h(1)=−5.3,h(n)=h(n−1)⋅(−11)\begin{cases} h(1)=-5.3, h(n)=h(n-1)\cdot(-11) \end{cases} Find an explicit formula for h(n)h(n). h(n)=h(n)=
  1. Given initial value: We are given the initial value h(1)=−5.3h(1) = -5.3 and the recursive formula h(n)=h(n−1)×(−11)h(n) = h(n-1) \times (-11). To find an explicit formula for h(n)h(n), we need to express h(n)h(n) in terms of nn without the need for previous terms.
  2. Apply recursive formula: Let's start by applying the recursive formula to the first few terms to see if we can identify a pattern.\newlineh(1)=−5.3h(1) = -5.3\newlineh(2)=h(1)×(−11)=−5.3×(−11)h(2) = h(1) \times (-11) = -5.3 \times (-11)\newlineh(3)=h(2)×(−11)=(−5.3×(−11))×(−11)h(3) = h(2) \times (-11) = (-5.3 \times (-11)) \times (-11)\newlineWe can see that each term is the previous term multiplied by −11-11.
  3. Generalize the pattern: Now let's generalize this pattern. For h(n)h(n), we multiply the initial value −5.3-5.3 by −11-11, (n−1)(n-1) times.\newlineh(n)=−5.3×(−11)(n−1)h(n) = -5.3 \times (-11)^{(n-1)}\newlineThis is the explicit formula for h(n)h(n).

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