Answer:
Step-by-step explanation:
<h3>Derivative </h3>
Since, the derivative of e^x is e^x and e^(yx) is ye^(yx)
That would be the commutative property
<h3>
Answer: </h3>
n starts at 1, and n is a positive whole number (1,2,3,...)
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Explanation:
The sequence is arithmetic with first term 40 and common difference 10. Meaning we add 10 to each term to get the next one.
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a1 = 40 = first term
d = 10 = common difference
is the general nth term of this arithmetic sequence
Plug in n = 1 and you should get
Plug in n = 2 and you should get
and so on
This is a geometric sequence with first term 1 and common ratio -1/2. r=-1/2.
a(n) = a(1)*(r)^(n-1).
Check: If n=2 our formula must return -1/2. Does it?
a(2) = 1(-1/2)^(2-1) = (-1/2)^1 = - 1/2. Yes.
a(3) should be 1/4. Is it? a(3) = (-1/2)^(3-1) = 1/4 Yes.
Then a(8) = (-1/2)^(8-1) = (-1/2)^7 = -1 / 2^7 = -1/128 (answer)