Chapter 7.8, Problem 48PPE

To determine

To find: Whether the sequence $1,2,3,5,\dots$ is arithmetic, geometric or neither.

Answer to Problem 48PPE

The sequence $1,2,3,5,\dots$ is neither arithmetic nor geometric.

Explanation of Solution

Given:

The sequence is $1,2,3,5,\dots$ .

Calculation:

Subtract the first term from the second term of the sequence to obtain the difference of sequence.

  $2-1=1$

Subtract the second term from the third term of the sequence to obtain the difference of sequence.

  $3-2=1$

Subtract the third term from the fourth term of the sequence to obtain the difference of sequence.

  $5-3=2$

Difference is not same; therefore, it is not an A.P.

Divide the second term with the first term of the sequence to obtain the ratio of sequence.

  $\frac{2}{1}=2$

Divide the third term with the second term of the sequence to obtain the ratio of sequence.

  $\frac{3}{2}=1.5$

Ratio is not same; therefore, the sequence is not a GP.

Thus, the sequence $1,2,3,5,\dots$ is neither arithmetic nor geometric.