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Find the 8th term of the geometric sequence 5, -15, 45, ...5,−15,45,...​

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Answer:

The 8th term of the geometric sequence 5, -15, 45, ... is:


a_8=-10935

Explanation:

Given the geometric sequence

5, -15, 45, ...

The first element of the geometric sequence is


a_1=5

A geometric sequence has a constant ratio 'r' and is defined by


a_n=a_1\cdot r^(n-1)

computing the ratios of all the adjacent terms


(-15)/(5)=-3,\:\quad (45)/(-15)=-3

The ratio between all the adjacent terms is the same and equal to


r=-3

substituting
a_1=5, and
r=-3 in the nth term


a_n=a_1\cdot r^(n-1)


a_n=5\left(-3\right)^(n-1)

Determining the 8th term:

We have already got the nth term


a_n=5\left(-3\right)^(n-1)

substituting n = 8 to determine the 8th term


a_n=5\left(-3\right)^(n-1)


a_8=5\left(-3\right)^(8-1)


a_8=5\left(-3^7\right)


a_8=-5\cdot \:3^7


a_8=-5\cdot \:2187


a_8=-10935

Therefore, the 8th term of the geometric sequence 5, -15, 45, ... is:


a_8=-10935

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