Question

Find an explicit rule for the nth term of the sequence.

7, -7, 7, -7, ...
MEDALS!!!!
GET YOUR MEDALS!!

Answer 1

is it an = 7 • (-1)n

Answer 2

as in times

Answer 3

a sub n = 7 * (-1)^n

Answer 4

Did you mean this?
\[\Large a_n = 7(-1)^{n}\]

Answer 5

yes

Answer 6

oh nvm, you wrote `a sub n = 7 * (-1)^n` which is close. Normally n starts at n = 1 to indicate the first term

n = 0 could be the starting point but then the count gets thrown off (eg: n = 3 refers to the fourth term, not the third, a bit confusing I know)

Answer 7

since n = 1 is a more natural starting point, you have to change that 'n' to 'n-1'

so the nth term formula is

\[\Large a_n = 7(-1)^{n-1}\]
where n starts at n = 1 and n is an integer

Answer 8

okay so thats the answer then?

Answer 9

yes

Answer 10

and thats because when you substitute 1 for n it refers to the second number in the sequence right

Answer 11

no, again it's more natural to say "n = 1 refers to the first term"

Let's see what happens when we plug in n = 1

\[\Large a_n = 7(-1)^{n-1}\]
\[\Large a_1 = 7(-1)^{1-1}\]
\[\Large a_1 = 7(-1)^{0}\]
\[\Large a_1 = 7(1)\]
\[\Large a_1 = 7\]

so 7 is our first term, which matches up with what the sequence gives us

Answer 12

Let's try n = 2
\[\Large a_n = 7(-1)^{n-1}\]
\[\Large a_2 = 7(-1)^{2-1}\]
\[\Large a_2 = 7(-1)^{1}\]
\[\Large a_2 = 7(-1)\]
\[\Large a_2 = -7\]

and we get -7 as our second term, as expected

Answer 13

oh okay thank you i got confused because i put that (-1)^0 equaled -1 and not 1

Answer 14

I used the rule

\[\Large x^0 = 1\]

where x is not equal to zero and x can be equal to any other number

Answer 15

thank you!!!

Answer 16

you're welcome