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h(n)=-91*(-(1)/(7))^(n-1) Complete the recursive formula of h(n). {:[h(1)=],[h(n)=h(n-1).]:}

h(n)=−91⋅(−17)n−1 h(n)=-91 \cdot\left(-\frac{1}{7}\right)^{n-1} \newlineComplete the recursive formula of h(n) h(n) .\newlineh(1)=□h(n)=h(n−1)⋅□ \begin{array}{l} h(1)=\square \\ h(n)=h(n-1) \cdot \square \end{array}

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Q. h(n)=−91⋅(−17)n−1 h(n)=-91 \cdot\left(-\frac{1}{7}\right)^{n-1} \newlineComplete the recursive formula of h(n) h(n) .\newlineh(1)=□h(n)=h(n−1)⋅□ \begin{array}{l} h(1)=\square \\ h(n)=h(n-1) \cdot \square \end{array}
  1. Identify First Term: Identify the first term of the sequence.\newlineTo find the recursive formula, we need to establish the first term, h(1)h(1).\newlineh(1)=−91×(−(1)/(7))(1−1)h(1) = -91 \times (-(1)/(7))^{(1-1)}\newline =−91×(−(1)/(7))0= -91 \times (-(1)/(7))^0\newline =−91×1= -91 \times 1\newline =−91= -91
  2. Determine Common Ratio: Determine the common ratio of the sequence.\newlineThe common ratio is the factor that each term is multiplied by to get the next term. In this case, the common ratio is the base of the exponent, which is −17-\frac{1}{7}.
  3. Write Recursive Formula: Write the recursive formula using the first term and the common ratio.\newlineThe recursive formula for a geometric sequence is h(n)=h(n−1)×rh(n) = h(n-1) \times r, where rr is the common ratio.\newlineFor this sequence, the recursive formula is:\newlineh(n)=h(n−1)×(−17)h(n) = h(n-1) \times (-\frac{1}{7})
  4. Combine First Term and Formula: Combine the first term and the recursive formula.\newlineThe complete recursive formula for the sequence is:\newlineh(1)=−91h(1) = -91\newlineh(n)=h(n−1)×(−17)h(n) = h(n-1) \times (-\frac{1}{7}) for n>1n > 1

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