Mathematics: a sequence has a first number of 3 and a half common difference of 4 what is the recursive rule of nth term

(F*g) means f ( g(x) ) . Knowing this we can say F(g(x)) = 3(5-x) ^2 = 3 (5-x)(5-x) =...

a sequence has a first number of 3 and a half common

Ответ:

natachalebrun2

14.02.2022

Mathematics

f(n) = f(n-1) + 8 for n 1

Step-by-step explanation:

Given

f(1) = 3 -- First Term

$\frac{1}{2}d = 4$ --- half common difference

Required

Find the recursive rule

First, we calculate the common difference

$\frac{1}{2}d = 4$

Multiply through by 2

$2 * \frac{1}{2}d = 2 * 4$

d = 8

The second term of the sequence is:

f(2) = 3 + 8 = 11

The third term is:

f(3) = 11 + 8 = 20

So, we have:

f(1) = 3

f(2) = 3 + 8

Substitute f(1) for 3

f(2) = f(1) + 8

Express 1 as 2 - 1

f(2) = f(2-1) + 8

Substitute n for 2

f(n) = f(n-1) + 8

Similarly:

f(3) = 11 + 8

Substitute f(2) for 11

f(3) = f(2) + 8

Express 2 as 3 - 1

f(3) = f(3-1) + 8

Substitute n for 3

f(n) = f(n-1) + 8

Hence, the recursive is:

f(n) = f(n-1) + 8 for n 1

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a sequence has a first number of 3 and a half common difference of 4 what is the recursive rule of nth term

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