Question

F(n)=−11+22(n−1), left parenthesis, n, right parenthesis, equals, minus, 11, plus, 22, left parenthesis, n, minus, 1, right parenthesis Complete the recursive formula of f(n), left parenthesis, n, right parenthesis.

Answer 1

The actual answer is g(1)=1

g(n)=g(n−1)+5

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Explanation:

Answer 2

`a_1 = -11\\\\a_n = a_((n - 1)) + 22`

Explanation:

An arithmetic sequence is generally given as:

f(n) = a + (n - 1)d

where a = first term and f(n) = nth term, d = common difference

The explicit formula given is:

f(n) = 11 + 22(n - 1)

The recursive formula is made of two statements, the first term and the formula showing how successive terms are related.

Mathematically, it is given as:

`a_1 = a\\\\a_n = a_((n - 1)) + d`

Therefore, the recursive formula is:

`a_1 = -11\\\\a_n = a_((n - 1)) + 22`