Question

Determine if the sequence below is arithmetic or geometric and determine the common difference/ratio in simplest form.

5,6,7

Answer 1

The given sequence, 5, 6, 7, ..., is arithmetic with a common difference of 1. Therefore, it is an arithmetic sequence, and the common difference is 1.

The given sequence, 5, 6, 7, ... is an arithmetic sequence. In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. In this case, the common difference is 1, as each term increases by 1.

Therefore, the sequence is arithmetic, and the common difference is 1.

An arithmetic sequence can be expressed as
`\(a_n = a_1 + (n-1)d\)`, where

`\(a_n\)` is the nth term,
`\(a_1\)` is the first term, n is the term number, and d is the common difference.

For the given sequence, the formula becomes
`\(a_n = 5 + (n-1) * 1\)`.

Alternatively, you can state: "This is an arithmetic sequence, and the common difference is 1." This succinctly conveys the nature of the sequence and the constant increment between consecutive terms.

Que. Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.. 5, 6, 7,...
This is............. sequence and the............ is equal to.............