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Complete the recursive formula of the geometric sequence 10, 6, 3.6, 2.16, ....

a(1) = a(n) = a(n − 1).​

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The common ratio (r) of this geometric sequence is found by dividing any term by its preceding term, such as:

r = a2/a1 = 6/10 = 0.6

We can use this common ratio to find any term in the sequence using the recursive formula:

a(n) = r * a(n-1)

where a(1) is the first term in the sequence, a(n) is the nth term, and a(n-1) is the (n-1)th term

Using this formula, we can find any term in the sequence. For example:

a(2) = r * a(1) = 0.6 * 10 = 6

a(3) = r * a(2) = 0.6 * 6 = 3.6

a(4) = r * a(3) = 0.6 * 3.6 = 2.16

and so on

Therefore, the complete recursive formula for this geometric sequence is:

a(n) = 0.6 * a(n-1), where a(1) = 10 and a(n) = a(n-1) for all n > 1

User Amit Chintawar
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