Question

Learning about Geometric Sequences.

How to find the nth term of a sequence?

Answer 1

http://aplus.sccpss.com/R85Content/media/pictures/ac_trig/d3011s1.gif?ts=1405343294480

Answer 2

Don't understand that..

Answer 3

@ganeshie8

Answer 4

A sequence is a series of sums.
\[\sum_{n=1}^{\infty}\]

The value of the term you add up each time depends on the value of n that rises per 1. The term usually consists of a coefficient (a_number) and an unknown (r).

so what you got as information in what you showed you could write as

if n=1 -> the term is a1 or a1(r)^0
if n =2 -> the term is equal to a1(r)
if n=3 -> the term is equal to a1(r)²
if n=4 -> the term is equal to a1(r)³
and so on...

if you write it as a sum you would get y(total)=a1 + a1(r) +a1(r)² + a1(r)³+....

instead of writing the sum of terms like above into infinity you can see a pattern

the coefficient is always a1 multiplied by r to a power. And if you look closer you'll notice that the power of r is always n-1.

For y of the nth-term (to infinity) you could say that y_n=a1(r)^(n-1)

But what we use as a letter for n is arbitrary... we can also use x, and make it

y_x=a1(r)^(x-1)

Answer 5

Sorry, that should be a_y=a1(r)^(x-1)

It's confusing because they suddenly use y and x. I would normally write it down as

a_n=a1(r)^n-1