Question

Explain why the sequence 4, 5, 7, 10, 14, … is not arithmetic.

Short answer

The difference between consecutive terms is not same.

Step-by-step solution

Step 1. Given Information.

The given sequence is 4, 5, 7, 10, 14, …

Step 2. Explanation.

A sequence is said to be arithmetic when the difference between the consecutive terms is always the same.

Here the difference between the first two terms is $5-4=1$

The difference between the next two terms is $7-5=2$

The difference between the next two terms is $10-7=3$

The difference between the next two terms is $14-10=4$

Here the difference between the consecutive terms is not the same. Hence the sequence is not arithmetic.

Step 3. Conclusion.

The difference between consecutive terms is not same.