Question

Help with arithmetic/geometric sequences and series problem please

Answer 1

The problem is in the attached file

Answer 2

what does is mean by describe the four quantities? Don't the quantitates mean the same thing in all four formulas?

Answer 3

the quantities are the the variables
like a_1,n,d,a_n in the problem a
and a_1,n,r,a_n in problem c

Answer 4

do you know what a_1 means?

Answer 5

the subscript there basically tells you

Answer 6

for example a_6 is the 6th term in the sequence

Answer 7

which choice a or c represents an arithmetic sequence ?
and of those choices one if a geometric sequence.

an example of an arithmetic sequence is 3,7,11,15,...
notice each term minus it's previous is the same number
this number is the common difference

an example of a geometric sequence is 2,4,8,16,...
notice each term divided by its previous is the same number
this number is the common ratio


what do you think the d represents ?
what do you think the r represents?

Answer 8

d represents the difference and r represents the common ratio @freckles

Answer 9

great d represents the common difference of an arithmetic sequence
and r represents the common ratio of a geometric sequence

Answer 10

I'm confused though because in the problem it says to describe the four quantities for each formula, but would the quantities be the same in each formula

Answer 11

for example wouldn't a_1 mean the first term in the sequence no matter what formula it is?

Answer 12

@freckles

Answer 13

yes a_1 can mean the first term in the sequence

Answer 14

ok, so how do I answer the second part of the question? @freckles

Answer 15

I don't know which 3 to use
for example in a
do they want us to use a_1, n, and d to find a_n
or
do they want us to use a_1,a_n,n to find d
or
do they want us to use a_n,n,d to find a_1
or
do they want us to use a_1,a_n,d to find n
or
do they want us to do each possibility of what they could mean

Answer 16

I'm not sure about that either, I'm assuming they want us todo each possibility. Could you just show me how to do it for 1 of the formulas and I can figure it out for the other ones? @freckles

Answer 17

\[a_n=a_1+d(n-1) \\ \text{ if we have } a_1,d, \text{ and } n \text{ just follow the order of operations \to find } a_n \\ \\ a_n=a_1+d(n-1) \\ \\ \text{ if we have } a_n,a_1,n \text{ then we can find } d \text{ by doing } \\ a_n-a_1=d(n-1) \text{ subtract } a_1 \text{ on both sides } \\ \frac{a_n-a_1}{n-1}=d \text{ divided both sides by} (n-1) \\ \]
then you can do something similar for the other two possibilties
just solve the equation for n
also solve the equation for a_1

Answer 18

ok so it's pretty simple

Answer 19

thanks!