Help me with this asap

a[25]=1.7, d=0.6

In general,

a[n] = a[1] + d(n-1)

1.7 = a[25] = a[1] + 0.6(25 - 1)

a[1] = 1.7 - 0.6(24) = -12.7

a[n] = -12.7 + 0.6(n - 1)

Answer a[1]=-12.7

Filling in the boxes,

a[1]=-12.7, a[2]=-12.1, a[3]=-11.5, a[4]=-10.9, a[5]=-10.3, a[6]=-9.7

check that last one with the formula, a[6]=-12.7-.6(6-1) = -9.7, good

we're asked for a recursive formula, which is easier,

a[n] = a[n-1] + 0.6

a[n] = a[1] + d(n-1)

a[23] = 21 = a[1] + 22d

a[43] = 61 = a[1] + 42d

Subtracting,

40 = 20d

d = 2

21 = a[1] + 22(2)

a[1] = 21 - 44 = -23

a[1] = -23,  a[n] = a[n-1] + 2

Check: a[n]=-23 + 2(n-1) at n=43 gives a[43]=-23 +2(42) =61, good

i pretty sure it is

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!