Question

Given the recursive formula below, what are the first 4 terms of the sequence? A) 17, –6, –3, 0B) 17, 13, 9, 5C) 17, 19, 21, 23D) 17, 15, 13, 11

Answer 1

`D)17,15,13,11`

Step-by-step explanation

Step 1

we have the recursive formula

`f(x)=\begin{cases}f(1)=17 \\ f(n)=f(n-1)-2\text{ if n }>1\end{cases}`

A recursive formula is a formula that defines each term of a sequence using the preceding term(s), we can see in the formula that the new term ( f(n)) equals the previous term minus 2

so

`\begin{gathered} f(1)=17 \\ hence \\ f(n)=f(n-1)-2 \\ \text{for n=2} \\ f(2)=f(2-1)-2 \\ f(2)=f(1)-2 \\ f(2)=17-2=15 \\ so,\text{ the second term is 15} \end{gathered}`

and so on,

Now for n=3

`\begin{gathered} f(n)=f(n-1)-2 \\ f(3)=f(3-1)-2 \\ f(3)=f(2)-2 \\ f(3)=15-2=13 \\ so,the\text{ second third terms i s13} \end{gathered}`

for n=4

`\begin{gathered} f(n)=f(n-1)-2 \\ f(4)=f(4-1)-2 \\ f(4)=f(3)-2 \\ f(4)=13-2=11 \\ \text{hence, the fourth term is 11} \end{gathered}`

so, the answer is

D) 17,15,13,11

I hope this helps you