Help with Arithmetic and Geometric Sequences?

Question

I'm studying Arithmetic Sequences and Geometric Sequences and I'm a little confused as to how I would figure out a few of the following problems. Any assistance would be appreciated!

Find the 7th term of the given sequence an = n(n + 2).

Find the first four terms of the given sequence an = (-1)n(n).

Find the 10th term of the given sequence an = (-1)n+1/n

and finally,

Find a formula for an, so that the first four terms are -1/2, ¼,-1/8, 1/16.

Again, any help is appreciated! Thanks!

I don't necessarily need the answers, moreso a method to solve the problems so that I understand the material. Thanks again!

Answer 1

probably, your questions should read:
a(n) = n(n + 2).
a(n) = (-1)n(n)
a(n) = (-1)n+1/n

then
n = the term
to find the first term, let n = 1
n =2, second term.
n=7, 7th term, etc.

Find the 7th term of the given sequence
a(n) = n(n + 2) means
a(7) = 7 (7+2) = 7 * (9) = 63

Find the first four terms of the given sequence
a(n) = (-1)n(n)

means find
a(1) = (-1) 1 (1)
a(2) = (-1) 2 (2)
a(3) = (-1) 3 (3)
a(4) = (-1) 4 (4)

etc.

Answer 2

a(n) = n(n + 2)
a(7) = 7(7+2) = 7*9= 63
so the 7th term is 63.

For a(n) = (-1)n(n), and a(n) = (-1)n+1/n, you also simply plug in the value of n that you want. (The first for terms are when n = 1, 2, 3, and 4.)

-1/2, ¼,-1/8, 1/16
comes from a(n) = (-1/2)^n

I hope this helps!

Answer 3

the key is n. make n=7 to get 7th term
part 2 to find the first 4 term plug in n=1 then n=2...3..4
part 3 plug in n=10 for 10th term
part 4 1/(-2)^n works

be careful some times n starts at 0 so the nth term is one less
the 10th term, if n starts at 0 not 1, is n=9

Answer 4

Just plug in 7 gettimg 7(7+2) = 789 = 63

(-1)^n (n) = -1, 2, -3, 4 [(-1)^n makes the signs alternate]

1/10 [It's positive because n is even

(-1)^n (1/2^n)