h(n)=-10 + 12n\ncomplete the recursive formula of h(n).\nh(1)=\n\nh(n)=h(n - 1)+\n
h(n)=-10 + 12n\ncomplete the recursive formula of h(n).\nh(1)=\n\nh(n)=h(n - 1)+\n
Answer
Explanation:
Step1: Find h(1)
Substitute n = 1 into $h(n)=- 10 + 12n$. $h(1)=-10+12\times1=-10 + 12=2$
Step2: Find the common - difference
We know that a linear function $h(n)=a+bn$ (in this case $a=-10$ and $b = 12$) can be written as a recursive formula $h(n)=h(n - 1)+b$. Since $h(n)=-10 + 12n$ and $h(n-1)=-10+12(n - 1)=-10+12n-12$, then $h(n)-h(n - 1)=(-10 + 12n)-(-10+12n - 12)=12$.
Answer:
$h(1)=2$ $h(n)=h(n - 1)+12$