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1. Use the information given to identify the a(8) term of the geometric sequence: a(2) = 5, r = -2.

User Marie Dm
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We have a geometric sequence, with a(2) = 5 and r = -2.

We can write geometric sequences in general as:


\mleft\lbrace a,a\cdot r,a\cdot r^2,a\cdot r^3,\ldots,a\cdot r^(n+1),\ldots\mright\rbrace

So we can write the second term, a(2), as:


a(2)=a\cdot r

As we know a(2) and r, we can calculate the base "a" as:


a=(a(2))/(r)=(5)/(-2)=-(5)/(2)

Any term can be calculated as:


a(n)=a\cdot r^(n-1)=(-(5)/(2))\cdot(-2)^(n-1)

Then, the eight term a(8) can be then calculated as:


a(8)=(-(5)/(2))\cdot(-2)^(8-1)=(-(5)/(2))\cdot(-2)^7=(-(5)/(2))\cdot(-128)=320

Answer: a(8) = 320

User Iiro Krankka
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