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:

$a=\frac{a(2)}{r}=\frac{5}{-2}=-\frac{5}{2}$

Any term can be calculated as:

$a(n)=a\cdot r^{n-1}=(-\frac{5}{2})\cdot(-2)^{n-1}$

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

$a(8)=(-\frac{5}{2})\cdot(-2)^{8-1}=(-\frac{5}{2})\cdot(-2)^7=(-\frac{5}{2})\cdot(-128)=320$

Answer: a(8) = 320