Answered

Get the answers you've been searching for with IDNLearn.com. Get accurate answers to your questions from our community of experts who are always ready to provide timely and relevant solutions.

What is the value of the fourth term in a geometric sequence for which [tex]a_1 = 10[/tex] and [tex]r = 0.5[/tex]?

Answer here: ______________________

Sagot :

GinnyAnsweridn
To find the fourth term in a geometric sequence, we'll use the formula for the nth term of a geometric sequence, which is given by:

[tex]\[ a_n = a_1 \cdot r^{(n-1)} \][/tex]

Here:
- [tex]\( a_1 \)[/tex] is the first term of the sequence.
- [tex]\( r \)[/tex] is the common ratio.
- [tex]\( n \)[/tex] is the term number you want to find.

Given:
- [tex]\( a_1 = 10 \)[/tex]
- [tex]\( r = 0.5 \)[/tex]
- [tex]\( n = 4 \)[/tex]

We need to find the fourth term ([tex]\( a_4 \)[/tex]).

Let's substitute the given values into the formula:

[tex]\[ a_4 = 10 \cdot (0.5)^{(4-1)} \][/tex]

Simplify the exponent:

[tex]\[ a_4 = 10 \cdot (0.5)^3 \][/tex]

Calculate [tex]\( (0.5)^3 \)[/tex]:

[tex]\[ (0.5)^3 = 0.5 \times 0.5 \times 0.5 = 0.125 \][/tex]

Now multiply by the first term ([tex]\( a_1 \)[/tex]):

[tex]\[ a_4 = 10 \cdot 0.125 \][/tex]

[tex]\[ a_4 = 1.25 \][/tex]

Therefore, the value of the fourth term in the geometric sequence is:

[tex]\[ 1.25 \][/tex]
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.