Question
Give an explicit formula for the th term of the following sequence. Do not include " " in your answer

Ask by Stanley Elliott. in the United States

Mar 19,2025

Question

Question Give an explicit formula for the $$ n $$th term of the following sequence. Do not include " $$ a_{n}= $$ " in your answer $$ a_{1}=8, a_{n}=-5 a_{n-1} \text { for } \mathrm{n} \geq 2 $$

UpStudy AI · Accepted Answer

1. Recognize that the recurrence relation is geometric since each term is obtained by multiplying the previous term by a constant ratio.

2. The general explicit formula for a geometric sequence is given by  
   $$
   a_{n} = a_{1} r^{n-1}
   $$
   where $$ a_{1} $$ is the first term and $$ r $$ is the common ratio.

3. Here, $$ a_{1} = 8 $$ and the common ratio $$ r = -5 $$.

4. Substitute these values into the formula to obtain  
   $$
   8(-5)^{n-1}
   $$
The $$ n $$th term is $$ 8 \times (-5)^{n-1} $$.

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Give an explicit formula for the th term of the following sequence. Do not include " " in your answer

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Question Give an explicit formula for the th term of the following sequence. Do not include " " in your answer