Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1?

Mathematics

2 answers:

Liono4ka [1.6K]2 years ago

8 0

Answer:

optian 2

Step-by-step explanation:

Trava [24]2 years ago

4 0

f (n + 1) = f(n) – 5 is the recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1

<h3>Solution:</h3>

Given that,

f(1) = 6 and n ≥ 1

Given sequence is 6, 1, -4, -9, -14

Let us first analyse the logic used in this sequence

6 - 5 = 1

1 - 5 = -4

-4 - 5 = -9

-9 - 5 = -14

Thus the next terms in sequence are obtained by subtracting 5 from previous term

Thus a recursive formula can be formed as:

f (n + 1) = f(n) – 5

Where "n" is the nth term

Let us check our recursive formula:

f(1+ 1) = f(1) - 5

f(2) = f(1) - 5

f(2) = 6 - 5 = 1

Thus we have got f(2) = 1 which is correct as per given sequence

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