~~((this is multiple choice and i raised the points))~~

what is the 10th term of the sequence 1/4, 1, 4, 16, 64, . . . ?

a) 1,024
`
b) 4,096
`
c) 16,348
`
d) 65,536

Multiply each term by 4 to get the 10th term.

d

1. there is a common difference of 4, so ur next terms are 13,17

2. there is a common difference of -2

3. A(n) = -14 + (n-1) * 2...n = 9

   A(9) = -14 + (9-1) * 2

   A(9) = -14 + 8 * 2

   A(9) = -14 + 16

   A(9) = 2

4. f(n) = 3 + 4(n-1)

yo n igga Miles Wilson☺☻

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!