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shusha [124]
3 years ago
10

1,a) Find a recursive formula for the sequence 1, 2, 6, 24, 120, . . . .

Mathematics
1 answer:
miss Akunina [59]3 years ago
3 0

a) The <em>n</em>-th term in the sequence is the product of the first <em>n</em> natural numbers:

1 • 2 = 2

1 • 2 • 3 = 6

1 • 2 • 3 • 4 = 25

1 • 2 • 3 • 4 • 5 = 120

and so on. Recursively, the <em>n</em>-th term is a function of the (<em>n</em> - 1)-th term as

<em>a(n)</em> = <em>n</em> <em>a(n</em> - 1<em>)</em>

<em />

b)<em> </em>Using the rule above, the 6th and 7th terms are

<em>a</em> (6) = 6 <em>a</em> (5) = 6 • 120 = 720

and

<em>a</em> (7) = 7 <em>a</em> (6) = 7 • 720 = 5040

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Step-by-step explanation:

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