Answer :

Final Answer:

The explicit formula for the given geometric sequence is[tex]\(a_n = -25 \cdot (-2)^{n-1}\).[/tex]

Explanation:

In a geometric sequence, each term is found by multiplying the previous term by a constant ratio. In this sequence, each term is half of the previous term. To find the explicit formula, we can start with the first term and observe the pattern:

- First term: -25

- Second term: [tex]-25 * (-2) = -50[/tex]

- Third term: -[tex]50 * (-2) = -100[/tex]

- Fourth term: -[tex]100 * (-2) = -200[/tex]

We can see that each term is obtained by multiplying the previous term by -2. Therefore, the common ratio [tex](\(r\))[/tex] in this geometric sequence is -2.

The formula for the nth term of a geometric sequence is given by[tex]\(a_n = a_1 \cdot r^{n-1}\),[/tex] where [tex]\(a_n\)[/tex] is the nth term, [tex]\(a_1\)[/tex] is the first term,[tex]\(r\)[/tex] is the common ratio, and [tex]\(n\)[/tex] is the term number.

In this case, [tex]\(a_1 = -25\)[/tex] and[tex]\(r = -2\)[/tex], so the explicit formula for the sequence is[tex]\(a_n = -25 \cdot (-2)^{n-1}\).[/tex]

This formula allows you to find any term in the sequence by plugging in the value of [tex]\(n\)[/tex]. For example, if you want to find the 5th term, you would substitute[tex]\(n = 5\)[/tex] into the formula:

[tex]\(a_5 = -25 \cdot (-2)^{5-1} = -25 \cdot (-2)^4 = -25 \cdot 16 = -400\).[/tex]

So, the 5th term of the sequence is -400.

Learn more about geometric sequence

brainly.com/question/33243139

#SPJ11

Thanks for taking the time to read Find an explicit formula for the geometric sequence 25 50 100 200 ldots. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada