Question

How do you start this???

What is the closed form of a geometric sequence with ratio between consecutive terms 5 and inital term 10?

A. an = 5(2n)
B. an = 2(5n)
C. an = 5n + 5
D. an = 5n

Answer 1

ratio between consecutive terms 5
means each term is 5 times bigger than the one before it.

inital term 10 means it starts at 10
so the sequence is
10, 50, 250, 1250, ...

Answer 2

I would try each formula with n=1 and n=2 and see if I get 10 for n=1, and 50 for n=2

Answer 3

okay thank you so much!

Answer 4

the formula
http://www.mathsisfun.com/algebra/sequences-sums-geometric.html

you would use
\[ a r^{n-1} \]
with a=10, r= 5
\[ 10 5^{n-1} \]
we can change its form by doing this:
\[10\cdot 5^{n-1}= 10\cdot 5^n \cdot 5^{-1} \\
= 10 \cdot 5^n \cdot \frac{1}{5^1} \\= \frac{10}{5} \cdot 5^n \\= 2 \cdot 5^n
\]

Answer 5

ohhhh. just simplifying with algebra. i shouldve tried that. LOL.