Question

aₙ=2n+5 The nth term of a sequence is given. Determine if the series is arithmetic or geometric. Find the common difference or the common ratio.

Answer 1

The sequence is arithmetic with a common difference of 2.

Step-by-step explanation:

The given sequence is arithmetic.

To determine the common difference, we can compare two consecutive terms of the sequence.

Let's consider the terms an and an+1: an = 2n + 5 and an+1 = 2(n+1) + 5 = 2n + 2 + 5 = 2n + 7.

The difference between the terms an+1 and an is (2n + 7) - (2n + 5) = 2. Therefore, the common difference of the arithmetic series is 2.