Chapter 12.3, Problem 78AYU

To determine

To find: Whether the sequence is arithmetic, geometric or neither, find the common difference or common ratio and also find the sum of the first fifty terms if the sequence is arithmetic or geometric.

Answer to Problem 78AYU

Therefore, the sequence is neither arithmetic nor geometric.,

Explanation of Solution

Given information:

The series is $1,1,2,3,5,8,\mathrm{.....}$ .

Calculation:

Here, $a_1=1$ , $a_2=1$ , $a_3=2$ .

Calculate the common difference by taking difference of consecutive terms.

  $\begin{array}{l}{a}_2-a_1=1-1\\ =0\end{array}$

  $\begin{array}{c}{a}_3-a_2=2-1\\ =1\end{array}$

Since the difference of consecutive terms is not constant the sequence is not arithmetic.

Calculate the common ratio.

  $\begin{array}{c}\frac{a_2}{a_1}=\frac{1}{1}\\ =1\end{array}$

  $\begin{array}{c}\frac{a_3}{a_2}=\frac{2}{1}\\ =2\end{array}$

Since the ratio of consecutive terms is not same the sequence is not geometric.

Therefore, the sequence is neither arithmetic nor geometric.,