Chapter 6.5, Problem 43E

To determine

To compare the graphs of arithmetic sequences to the graphs of geometric sequences.

Answer to Problem 43E

The comparison has done between the graph of arithmetic sequence and the graph of geometric sequence.

Explanation of Solution

Given: The arithmetic sequences and geometric sequence is given.

Let’s say,

  $f(x)=2x+6$

x	1	2	3	4	5
f(x)	8	10	12	14	16

  

Therefore, the arithmetic sequences are: $\mathrm{......},\text{8,10,12,14,16,}\mathrm{.....}$

The properties of the arithmetic sequences are similar to properties of linear function.

Similarly, $f(x)=3\cdot 2^x$

x	1	2	3	4
f(x)	6	12	24	48

Therefore,the geometric sequences are: $\mathrm{......},6\text{,12,24,48,}\mathrm{.....}$

The properties of the geometric sequences are similar to properties of exponential function.

Hence,

The comparison has done between the graph of arithmetic sequence and the graph of geometric sequence.