The sequence 1, 3, 6, 10, 15, etc find dy/dx...
dy/dx=2,3,4,5 this is not a constant so find d2y/dx2
d2y/dx2=1,1,1, this is a constant, specifically a constant acceleration, which is a property of a quadratic function of the form ax^2+bx+c and if we use three points of the sequence we can solve for all of the variables...
9a+3b+c=6
4a+2b+c=3
a+b+c=1 getting differences
5a+b=3
3a+b=2 and again
2a=1, so a=1/2, making 3a+b=2 become:
1.5+b=2, so b=1/2, making a+b+c=1 become
1/2+1/2+c=1 so c=0 so our function is:
a(n)=(n^2+n)/2
which can be expressed, if you factor the numerator as:
a(n)=n(n-1)/2
Amount in the bank account = 1000(1 + 0.05)^5 = $1,276.28
We have that
3 = 3 + 0i -----------> rewrite as 3(1 + 0i)
<span>So now what we have to do is figure out which of the above expressions has cos a = 1 and sin a = 0. </span>
<span>cos 0 = 1, and sin 0 = 0, so that's the answer that we want.
</span><span>the answer is: </span>
3 = 3(cos 0 + i sin 0)
The answer to this would be
