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Answer:
The sum of the six terms is 9331
Step-by-step explanation:
* Lets explain what is the geometric sequence
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric sequence:
# U1 = a , U2 = ar , U3 = ar² , U4 = ar³ , U5 = ar^4
# , where a is the first term , r is the constant
ratio between each two consecutive terms, n is the position
of the term
- The sum of n terms of the geometric sequence is:
, where n is the number of the terms
a is the first term and r is the common ratio
* Lets solve the problem
∵ The geometric sequence is 1 , -6 , 36 , .........
∵ The common ratio r = U2/U1
∵ U1 = 1 and U2 = -6
∴ r = -6/1 = -6
∵ The first term is 1
∴ a = 1
∵ There are 6 terms in the sequence
∴ n = 6
∴ The sum =
* The sum of the six terms is 9331
Answer:
Maximum value of total revenue = 18
Step-by-step explanation:
- Express this Demand Curve in terms of Q.
<em>P = 24 - 8Q (it is the same equation)</em>
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- Find P, if Q=2
<em>P= 24-8(2)</em>
<em>P=24-16</em>
<em>P=8</em>
- Find Q if P = 8.
<em>P = 24 - 8Q</em>
<em>8= 24 - 8Q</em>
<em>8Q= 24-8</em>
<em>8Q=16</em>
<em>Q=16/8</em>
<em>Q=2</em>
- Total revenue in terms of Q
<em>Total revenue is P times Q, that is</em>
<em>P*Q=TR=(24-8Q)*Q</em>
<em>TR=24Q-8Q^2</em>
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- Marginal Revenue
<em>It is the first derivative of TR</em>
<em>TR'(Q)= 24-16Q</em>
- Find the values of P and Q that will maximize total revenue.
<em>To find them first TR'(Q)=0, that is</em>
<em>0=24-16Q</em>
<em>16Q=24</em>
<em>Q=24/16</em>
<em>Q=3/2</em>
<em>Q=1.5</em>
<em>and we plug in 1.5 in P=24-8Q, which is,</em>
<em>P=24-8Q</em>
<em>P=24-8(1,5)</em>
<em>P=24-12</em>
<em>P=12</em>
- Calculate this maximum value of total revenue
<em>P=12 Q=1.5</em>
<em>P*Q=Total Revenue</em>
<em>12*1.5=Total Revenue</em>
<em>18=Total Revenue</em>
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