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Resuelve los siguientes ejercicios de las sucesiones geométricas:

1. Encuentre la suma de los primeros 9 términos de la progresión geométrica [tex]\(4, 20, 100, \ldots\)[/tex]

2. ¿Cuál es el último término de la progresión geométrica donde el primer término es [tex]\(5\)[/tex], la razón es [tex]\(4\)[/tex] y tiene [tex]\(8\)[/tex] términos?

Sagot :

GinnyAnsweridn

Final answer:

The sum of the first 9 terms in a geometric progression and finding the last term based on the given values.


Explanation:

To find the sum of the first 9 terms of a geometric progression, we use the formula: Sum = a(1-r^n) / (1-r), where 'a' is the first term, 'r' is the common ratio, and 'n' is the number of terms. For the given progression 4, 20, 100,..., the common ratio is 5. The sum of the first 9 terms would be 3795. To find the last term of a geometric progression knowing the first term, common ratio, and number of terms, we use the formula: last term = first term * common ratio^(number of terms - 1). With the values given in the second question, the last term would be 81920.


Learn more about Geometric Progressions here:

https://brainly.com/question/4853032


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