Question

In a sequence.....

What is the difference between n-1 and just n?

For example, if I'm trying to find an explicit rule for the n term of "4, -4, 4, -4...."

would it be 4*(-1)^n ....... or......... 4*(-1)^n-1??

Answer 1

4 i believe

Answer 2

Well, the sign beside '4' depends on the nature of the power of '-1'.
If the power, say 'x' is even, the '-1' gets multiplied an even no. of times, and hence equals a '+1', hence, the 4 turns out to be positive. however, 'x-1', in such a case, would be odd - and '-1' multiplied odd no. of times would give you a '-4'!

Answer 3

In here, you start with an even 'n'. So, as hartnn just mentioned. As far as I remember you can start a sequence with n=0, which is even. Do confirm this though.

Answer 4

oh! so if it is an positive even number and you want to express it changing to a negative number you would use n-1 and if it is a positive even number and it doesn't change signs you just use n?? So then if it's a positive odd number and it changes to a negative you'd do the opposite?

Answer 5

I hope I read that right! :P

Answer 6

It's not about the base, (i.e. 4 in this case) - it's about the power of '-1', which we mutiply with the base to change its sign.

Answer 7

You can start with any value of n that you want, but convention is that you start with n = 1 because you can jump to say n = 12 and say to yourself "n = 12 generates the 12th term" or "n = 17 gives me the 17th term" etc etc

If you started with n = 0, then you would have to do a correction and say to yourself that "n = 5 is really the 4th term and not the 5th term". This correction is done because n = 0 is really the first term, n = 1 is the second and so on.

So this is why n = 1 is a natural starting point.

Answer 8

So because you naturally start at n = 1, you would use n - 1 over just n alone in the exponent.

Answer 9

but how do they start at n=1 if this one is just 4,-4,4,-4

Answer 10

the first term is 4

the common ratio is -1 since you're multiplying each term by -1 to get the next term

Answer 11

this means

first term: 4 ----> a = 4
common ratio: -1 ---> r = -1

Answer 12

then we plug the two into

an = a*r^(n-1)

to get

an = 4*(-1)^(n-1)

Answer 13

to get any term we want, we just plug in the correct value of n

so say we want the 3rd term, well we plug in n = 3 to get

an = 4*(-1)^(n-1)

a3 = 4*(-1)^(3-1)

a3 = 4*(-1)^(2)

a3 = 4*(1)

a3 = 4

and this matches with what the 3rd term really is: 4

Answer 14

Oh wow thank you! I didn't understand the whole common ratio part of it but that clears it up!

Answer 15

yeah the common ratio only applies if you multiply each term by the same number to get the next number and it would stay fixed throughout the entire sequence

you can't go from 4 to -4, then from -4 to 10 because the ratio would change...and not be so "common" anymore

Answer 16

oh okay! Thanks so much!

Answer 17

you're welcome