Chapter 6.5, Problem 11E

To determine

To find:Whether the sequence $9,14,20,\mathrm{27...}$ is arithmetic, geometric or neither.

Answer to Problem 11E

The sequence $9,14,20,\mathrm{27...}$ is neither arithmetic nor geometric.

Explanation of Solution

Given information:The sequence $9,14,20,\mathrm{27...}$

Calculation:A sequence is said to be arithmetic sequence if every term of the sequence, after the first term, is obtained by adding a constant to the preceding term. The constant is known as common difference.

A sequence is said to be geometric sequence if every term of the sequence, after the first term, is obtained by multiplying a constant to the preceding term. The constant is known as common ratio.

Here, the 1^st term $=9$

Difference between 1^st and 2^nd term $=14-9=5$

Difference between 2^nd and 3^rd term $=20-14=6$

Difference between 3^rd and 4^th term $=27-20=7$

Since, each term of the sequence is not obtained by adding a constant to the preceding term, the sequence is not arithmetic.

Again, the 1^st term $=9$

Dividing 2^nd term by 1^st term $=\frac{14}{9}=1.55$

Dividing 3^rd term by 2^nd term $=\frac{20}{14}=1.43$

Dividing 4^th term by 3^rd term $=\frac{27}{20}=1.35$

Since, each term of the sequence is not obtained by multiplying a constant to the preceding term, the sequence is not geometric.