Answered

What is the sum of the geometric sequence 1, 3, 9, … if there are 12 terms?


292,524


265,720


139,968


104,976

Verified Answer :

Greenleafable

The sum of this geometric sequence is 265, 720.
1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187 + 6561 + 19683 + 59049 + 177147 = 265, 720
You just multiply each number by 3 to find the sequence and then add those numbers. 

Answer:

The sum of the given geometric series if there are 12 terms is:

                                265,720

Step-by-step explanation:

We are given a geometric sequence as:

1,3,9,.....

This means that the common ratio(r) of the sequence is:  3

Since each term is increasing by a multiple of '3'

Also, sum of an finite geometric series with n terms is given by:

\(S_n=a\times (\dfrac{r^n-1}{r-1})\)

where n is the number of terms whose sum is calculated and a is the first term of the sequence.

We have n=12, a=1 and r=3

Hence, the sum is:

\(S_{12}=1\times (\dfrac{3^{12}-1}{3-1})\\\\\\S_{12}=\dfrac{531440}{2}\\\\\\S_{12}=265720\)

         Hence, the sum is:  265,720

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