18.5k views
0 votes
Find the sum of the first 8 terms of the following series, to the nearest integer.

12, 36, 108, ...

User Sean Riley
by
8.4k points

1 Answer

7 votes

Answer:

The sum of the first 8 terms is 39360

Explanation:

A geometric series is a series of numbers that have a common ratio. The series given to us is the following: 12, 36, 108,... We can see that there is a common ratio of 3 (108/36 = 36/12 = 3). Therefore, this series is a geometric series. Since we know that, we can use the sum of geometric series formula to find the sum of the first 8 terms:


S_n=(a_1(1-r^n))/(1-r)

In this formula,
S_n is the sum of the first n terms of the series (in our case, n would be 8).
a_1 is the first term in the series, which is 12 in our case. r is the common ratio between the terms (which is 3). Finally, n is the number of terms, and since we know we are looking for the sum of the first 8 terms, n is 8. Now, we can plug in our known quantities and solve:


S_n=(a_1(1-r^n))/(1-r)\\\\S_8=(12(1-3^8))/(1-3)\\\\S_8=(12(1-6561))/(-2)\\\\S_8=-6(-6560)\\\\S_8=39360

Therefore, the sum of the first 8 terms is 39360

User Anton Danilov
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories