Question

Arithmetic sequence is a sequence of terms that have a common ____ between them

Answer 1

Difference

Explanation:

Arithmetic sequences are given series' that have a constant difference between each entry in the sequence. For example, 3, 9, 15, 21, 27 is an arithmetic sequence with the common difference of 6. When given a sequence with 5 entries like this one, set up the equation by...

`\boxed{!}\:\:a_n=a_1+\left(n-1\right)d`

You want to use this equation to set up the arithmetic sequence. This defines the constant[common] difference. Next, add the ₙth term. The ₙth term is the term in an arithmetic sequence for any term, for instance, 21 in the sequence we are currently working on. Then, add the first entry by the common difference, which is multiplied by n - 1, where n is a placeholder term. Lastly, go by what you know. What we know: The common difference is 6.

`a_n=6\left(n-1\right)+3\\a_n=\left(n-1\right)\\a_n=6\left(n\right)+3\\a_n=6\left(n\right)\\a_n=6n-3`

Therefore,

`d=6,\:a_n=6n-3`

Hope this helps!