Use the formula to evaluate the series -3 + 6 - 12 +24 - ...-az.
1 answer:
Answer:
Your sum = - 1
S = ( (-2)^n - 1), If you let n = z, then S = (-2)^z - 1
Step-by-step explanation:
I can use a formula to find the sum of the first n terms.
we have -3, 6, -12, 24, ... etc.
common ratio = r = -2
first term = -3
a_1 = -3
Then: a_n = a_1 * r ^(n -1)
a_n = (-3) * (-2)^(n - 1) is the general formula for the nth term
Sum of first n terms = S = a_1 * (r^n - 1) / (r - 1)
so...
S = (-3) * ((-2)^n - 1 )/ (-2 - 1)
which simplifies to
S = (-3) *((-2)^n - 1) / (-3)
S = ( (-2)^n - 1)
If you let n = z, then S = (-2)^z - 1
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Answer:
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Step-by-step explanation:
Newtons law cooling describes the rate at which an exposed body changes temperature through radiation which is approximately proportional to the difference between the object’s temperature and its surroundings, provided the difference is small. The formula is given as:
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slope intercept form is y=mx+b
So slope intercept form is The office manager of a small office ordered 140 packs of printer paper based on average daily use, she knows that the paper will last about 80 days
(A) Lets make a table
X axis represents the Number of days paper used
y axis represents the packs of printer paper used
x y
days packs of printer paper used
0 0 (0 days , 0 packs used)
80 140 (in 80 days , 140 packs paper used)
The graph is attached below
(B) To find Equation of a line we use points (0,0) and (80,140)
y intecept is (0,0)
so b= 4
Slope intercept form of a line i y=mx + b
m is the slope and b is the y intercept
So slope intercept form of line becomes
Standard form is Ax + By =C
Multiply both sides by 4
4y = 7x
Now subtract 7x on both sides
-7x + 4y =0 is the standard form
(c) To find packs of printer paper the manager expect to have after 30 days, Plug in 30 for x and find out y
Total 140 packs of printer paper
52.5 packs of paper used
Packs of paper remaining after 30 days = 140- 52.5= 87.5
