How do I find the rule for the Nth Term? Check out these sequences... PLEASE!?

Question

How do I find the rule for these sequences? I just need to get some help, how do I figure these out? I've been thinking about it all day.... I just need some help.


Sequence #1:

N: 1, 2, 3, 4, 5

f(n): 7, 9, 7, 9, _?_

Rule: _?_

Sequence #2:

N: 1, 2, 3, 4, 5

f(n): -3, 6, -9, 12

Rule: _?_

Sequence #3:

N: 1, 2, 3, 4, 5

f(n): 1, 3, 6, 10, 15

Rule: _?_

Answer 1

#1 Odd N 7; even N 9

#2 Odd N multiply by -3; even N multiply by 3

#3 N(N+1)/2

Answer 2

Very, very interesting.
I tend to not follow the (if odd, if even) method of creating equations for the nth term. However, there isn't any mathematical method that I observe to solve Seq. 1 without using the if odd.../if even... method.

Sequence#1= ODD = 7[n-(n-1)] EVEN = 9[n-(n-1)]
Sequence #2= -1^n(3n)
Secquence#3= n(n+1) / 2

Answer 3

Very, very exciting. I quite have a bent to now no longer persist with the (if outstanding, if even) attitude of bobbing up equations for the nth term. even however, there is now no longer any mathematical attitude that I be huge unsleeping to resolve Seq. a million devoid of utilizing the if outstanding.../if even... attitude. series#a million= outstanding = 7[n-(n-a million)] EVEN = 9[n-(n-a million)] series #2= -a million^n(3n) Secquence#3= n(n+a million) / 2

Answer 4

for #1, f(n) = 7 if n is odd and f(n) = 9 if n is even.
for #2, f(n) = 3n(--1)^n = -- 3n if n is odd and f(n) = 3n if n is even.
for #3, f(n) = 1 + 2 + 3 + .... + (n --1) + n = n(n + 1)/2

Answer 5

seq #2 next number is -15

rule is (-1)^n x 3n