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Sequences help!!!

Can someone explain how to do this please?
By writing down the first terms or otherwise, find the recurrence formula that defines the following sequences:
Un = (-1)^n n
Reply 1
Avatar for dskinner
dskinner
2
Original post by Purpleunicorn197
Can someone explain how to do this please?
By writing down the first terms or otherwise, find the recurrence formula that defines the following sequences:
Un = (-1)^n n


is that

Un=(−1)n×nU_n = \left(-1\right)^n \times n ????
Original post by dskinner
is that

Un=(−1)n×nU_n = \left(-1\right)^n \times n ????


yes
Reply 3
Avatar for dskinner
dskinner
2
Original post by Purpleunicorn197
yes


Well finding the first term is easy, let n be any number.

put in 1
you get -1 out

put 2
you get -1 out

put in 64378268427916547924789136579824758931
you still get -1 out

but i don't quite understand the second part :/

@Zacken what would you do for the second bit?
Reply 4
Avatar for Zacken
Zacken
22
Original post by Purpleunicorn197
yes


Write out the sequence. You can see that U1=−1U_1 = -1, U2=2U_2 = 2, U3=−3U_3 = -3, U4=4U_4 = 4, etc...

i.e: to go from the first term to the second term, you need to multiply the result by -1 and then either add 1. To go from the second to the third, you need to multiply by -1 and then subtract 1.

So you should be thinking Un=−Un−1±1U_n = -U_{n-1} \pm 1 but you need to find a way to write the ±1\pm 1 such that it adds one when finding the second term (i.e: even cases) and subtracts one when finding odd terms. Think about it in terms of (−1)f(n)(-1)^{f(n)}.

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