Question

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

Answer 1

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