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Complete the recursive formula of the geometric sequence 300,60,12,2.4,dots.. d(1)= d(n)=d(n-1).

Complete the recursive formula of the geometric sequence \newline300,60,12,2.4,…300, 60, 12, 2.4, \dots\newlined(1)=d(1)= \newlined(n)=d(n−1)⋅d(n)=d(n-1)\cdot

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Full solution

Q. Complete the recursive formula of the geometric sequence \newline300,60,12,2.4,…300, 60, 12, 2.4, \dots\newlined(1)=d(1)= \newlined(n)=d(n−1)⋅d(n)=d(n-1)\cdot
  1. Identify First Term: Identify the first term of the sequence.\newlineThe first term of the sequence is given as 300300.
  2. Determine Common Ratio: Observe the pattern to determine the common ratio.\newlineThe sequence is 300300, 6060, 1212, 2.42.4, ... \newlineTo find the common ratio, divide the second term by the first term: 60300=0.2\frac{60}{300} = 0.2
  3. Write Recursive Formula: Write the recursive formula using the first term and the common ratio.\newlineThe recursive formula for a geometric sequence is given by:\newlined(n)=d(n−1)×rd(n) = d(n-1) \times r, where rr is the common ratio.\newlineHere, d(1)=300d(1) = 300 and r=0.2r = 0.2.\newlineSo, the recursive formula is d(n)=d(n−1)×0.2d(n) = d(n-1) \times 0.2.

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