Question

Write the explicit formula for the geometric sequence.

a1 = -5 a2 = 20 a3 = -80

Answer 1

It looks like each successive term is the previous one multiplied by -4, so that's the common ratio between terms. What do you know about the general form of a geometric sequence?

Answer 2

uhm nothing rellee

Answer 3

maybe you could just give me the answer?

Answer 4

A geometric sequence is of the form
\[\{ar^n\}\]
where r is the common ratio and n starts with, say, 0 and goes up by one for each successive term.

For example, the geometric sequence
\[\left\{2\left(\frac{1}{2}\right)^n\right\} = \left\{ 2, 1, \frac{1}{2}, \frac{1}{4},\ldots \right\}\]
So, when n = 0, you have 2,
n = 1, you get 1,
and so on.
(Each successive term is divided by 2, or multiplied by 1/2.)

For your sequence, clearly the first term (when n=0) is -5, and r = -4.
Think you can write up a general sequence using that info?

Answer 5

Giving you the answer would hardly help you understand what you're doing.

Answer 6

an = -5 • (-4)n ?

Answer 7

That's right. Just remember the n is an exponent.

Answer 8

ok wait i have another question tho!

Answer 9

What is it?

Answer 10

Write the recursive formula for the geometric sequence.

a1 = -2 a2 = 8 a3 = -32

Answer 11

Following the same process, I'd first write the sequence as a regular geometric sequence, which you should be able to understand is
\[a_n = -2 (-4)^n,\]
right?

Answer 12

riighhhht..

Answer 13

That means that
\[a_{n+1} = -2(-4)^{n+1}\]
If you're familiar with properties of exponents, you should be able to easily express a_(n+1) in terms of a_n.

Answer 14

nopee

Answer 15

\[a_{n+1} = -2(-4)^{n+1} = -2(-4)^n \cdot (-4)^1\]
Look familiar?

Answer 16

honestly noo...

Answer 17

Well, in any case, can you see that you can substitute a_n into that last equation? I gave you a_n earlier, so you shouldn't have any problems with finding it.