Chapter 11.1, Problem 18CYU

To determine

To evaluate whether sequence is arithmetic , geometric or neither.

Answer to Problem 18CYU

The sequence is neither arithmetic nor geometric

Explanation of Solution

Given: 5 , 1 , 7 , 3 , 9 ,....

Formula used;

For geometric sequence

  

where r is the common ratio

For arithmetic sequence

  

where d is the common difference

Calculation:

  $\begin{array}{l}{a}_1=5\\ a_2=1\\ a_3=7\\ a_4=3\\ a_5=9\\ \\ \text{For Geometric sequence}\\ r=\frac{a_2}{a_1}=\frac{1}{5}\\ r=\frac{a_3}{a_2}=7\\ \text{The common ratio is not same}\text{.}\\ \therefore \text{ the sequence is not geometric}\text{.}\\ \\ \text{For Arithemetic sequence}\\ \\ d=a_2-a_1\\ =1-5\\ =-4\\ d=a_3-a_2\\ =7-1\\ =6\\ \text{The common difference is not same}\text{.}\\ \therefore \text{ the sequence is not arithemetic}\text{.}\end{array}$

Interpretation:

The sequence is neither Geometric nor Arithmetic