Question

Arithmetic and Geometric Sequences

1. Consider the sequence: 3, 7, 11, 15...

Find an explicit formula for the n-th term of this sequence.
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Answer 1

Explanation:

This is arithmetic since adding 4 to each term gets us to the next term in the sequence. That means that the common difference, d, is 4. The general arithmetic explicit formula is

`a_n=a_1+d(n-1)` and using the info given when a1 = 3 and d = 4:

`a_n=3+4(n-1)` or, if you want to make it easier to deal with:

`a_n=4n-1` (I just distributed through the parenthesis and then combined like terms. As you can see, arithmetic sequences are linear).