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andrey2020 [161]
3 years ago
11

Find the explicit formula for the general nth term of the arithmetic sequence described below. Simplify your answer.

Mathematics
1 answer:
Alexandra [31]3 years ago
8 0

\boxed{a_{n}=-3+8(n-1)}

<h2>Explanation:</h2>

The explicit formula for the general nth term of the arithmetic sequence is given by:

a_{n}=a_{1}+d(n-1) \\ \\ \\ Where: \\ \\ a_{n}:nth \ term \\ \\ n:Number \ of \ terms \\ \\ a_{1}:First \ term \\ \\ d:common \ difference

Here we know that:

a_{1}=-3 \\ \\ a_{10}=69

So, our goal is to find the common difference substituting into the formula:

a_{10}=a_{1}+d(10-1) \\ \\ 69=-3+d(9) \\ \\ Solving \ for \ d: \\ \\ 9d=69+3 \\ \\ 9d=72 \\ \\ d=8

Finally, we can write the explicit formula as:

\boxed{a_{n}=-3+8(n-1)}

<h2>Learn more:</h2>

Geometric series: brainly.com/question/1509142

#LearnWithBrainly

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