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Complete the recursive formula of the geometric sequence 10,6,3.6,2.16,dots. a(1)= a(n)=a(n-1).

Complete the recursive formula of the geometric sequence \newline10,6,3.6,2.16,…10, 6, 3.6, 2.16, \dots.\newlinea(1)=a(1)= \newlinea(n)=a(n−1)⋅a(n)=a(n-1)\cdot

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Q. Complete the recursive formula of the geometric sequence \newline10,6,3.6,2.16,…10, 6, 3.6, 2.16, \dots.\newlinea(1)=a(1)= \newlinea(n)=a(n−1)⋅a(n)=a(n-1)\cdot
  1. Identify first term: We are given the sequence: 1010, 66, 3.63.6, 2.162.16, ...\newlineFirst, we need to identify the first term of the sequence, which is given as 1010.\newlineSo, a(1)=10a(1) = 10.
  2. Find common ratio: Next, we need to find the common ratio by dividing the second term by the first term.\newlineThe common ratio r=610=0.6r = \frac{6}{10} = 0.6.
  3. Write recursive formula: Now, we can write the recursive formula for the sequence using the first term and the common ratio.\newlineThe recursive formula is a(n)=a(n−1)×ra(n) = a(n-1) \times r, where rr is the common ratio.\newlineSubstituting the value of rr, we get a(n)=a(n−1)×0.6a(n) = a(n-1) \times 0.6.

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