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balandron [24]
3 years ago
12

Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15

Mathematics
2 answers:
Thepotemich [5.8K]3 years ago
7 0

Answer:

the summation of 4 times negative 3 to the n minus 1 power, from n equals 4 to 15.

Step-by-step explanation:

goblinko [34]3 years ago
3 0
a_n=5 \ for \ n=1 \\
a_n=-10 \ for \ n=2 \\
a_n=20 \ for \ n=3

You can see it's a geometric sequence because the ratio is constant (\frac{a_3}{a_2}=\frac{a_2}{a_1}).
The nth term of a geometric sequence:
a_n=a_1 \times r^{n-1}

a_1=5 \\
r=\frac{a_2}{a_1}=\frac{-10}{5}=-2 \\ \\
a_n=5(-2)^{n-1}

It has to be the sum for term 4 through term 15, so n=4 and the number above the sigma is 15.

Your answer:
\sum^{15}_{n=4} 5(-2)^{n-1}
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