5. Find the sum of the indicated number of terms in the geometric sequence with a1 = 5, r = -1 , n = 12
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5. Find the sum of the indicated number of terms in the geometric sequence with a1 = 5, r =
5. Find the sum of the indicated number of terms in the geometric sequence with a1 = 5, r = -1 , n = 12
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Answer:
The sum of the first 12 terms of the geometric sequence is 0.
Step-by-step explanation:
Given: [tex]a_1=5[/tex], [tex]r=-1[/tex], [tex]n=12[/tex]
Find: [tex]S_{12}=?[/tex]
Formula: [tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]
Solution:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}\\S_{12}=\frac{5[1-(-1)^{12}]}{1-(-1)}\\S_{12}=\frac{5(1-1)}{1+1}\\S_{12}=\frac{5(0)}{2}\\S_{12}=\frac{0}{2}\\S_{12}=0[/tex]
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