what is the sum of the geometric sequence -1, 6, -36, . . . if there are 6 terms?
Mathematics · High School · Tue Nov 03 2020
Answered on
Given the geometric sequence.
-1, 6, -36, …
Determine the sum if there are 6 terms.
Solution:
In order to determine the sum, we must first identify the 6th terms. Before that, we must also know first the common ratio, this can be done by dividing the second term with the first term.
1st term = -1
2nd term = 6
Common Ratio: r = 6 / -1
Common Ratio: r= -6
Now we need to determine the 6th term, in order to do so we will use the equation for geometric sequence.
An = A1( r)^n-1
A6 = -1 ( -6)^ 6-1
A6 = -1 ( -6)^ 5
A6 = - 1( -7776)
A6 = 7776
In order to find the sum of all 6 terms, we will use the formula,
Sn = (a1 (1 - r^n))/ 1 - r
Sn = (-1 ( 1- (-6)^6)/ 1 -(-6)
Sn = (- 1( 1 - 46656) / 1 + 6
Sn = (-1(-46655)/ 7
Sn = 46655/7
Sn = -6,665
The sum of the geometric sequence is -6,665.