Question

The first two numbers in a sequence areh(1) = 4 and h(2) = 8a) If h(x) is an arithmetic sequence, write anequation:b) If h(x) is a geometric sequence, write anequation:

Answer 1

First term of sequence (a)=4

Second term of sequence =8

The recursive defination of arithmatic sequence is,

$\begin{gathered} a_n=a_{n-1}+d \\ a_0=a=4 \\ \text{common difference d=8-4=4} \end{gathered}$

The arithmatic sequence is written as,

$\begin{gathered} h(x)=a_0+dn \\ h(x)=4+4n \\ h(x)=4,8,12,16 \end{gathered}$

The recursive defination of geometric series is,

$\begin{gathered} a_n=ra_{n-1} \\ \text{where a}_0=4 \\ 8=a_0r \\ 8=4.r \\ r=2 \\ \text{commom ratio = r=2} \end{gathered}$

The geometrix series is written as,

$\begin{gathered} a_n=a_{0^{}}r^n \\ h(x)=4(2)^n_{} \\ h(x)=4,8,16,\ldots\text{..} \end{gathered}$

Answer:

$\begin{gathered} 1)h\mleft(x\mright)=4+4n \\ 2)h(x)=4(2)^n \end{gathered}$