Use mathematical induction to prove that the statement is true for every positive integer n.12 + 42 + 72 + . . . + (3n - 2)2 = 
What will be an ideal response?
Answers will vary. One possible proof follows.
a). Let n = 1. Then, 12 = 
= 
= 1. So, the statement is true for n = 1.
b). Assume the statement is true for n = k:
Sk = 
.
Also, if the statement is true for n = k + 1, then
Sk+1 = Sk + (3(k + 1) - 2)2 = 
.
Subtract to get:
Sk+1 - Sk = (3(k + 1) - 2)2 = 
- 
Expand both sides and collect like terms:
9k2 + 6k + 1 = 
- 
9k2 + 6k + 1 = 
= 9k2 + 6k + 1
Since the equality holds, then the statement is true for n = k + 1 as long as it is true for n = k. Furthermore, the statement is true for n = 1. Therefore, the statement is true for all natural numbers n.
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Find the center, foci, and vertices of the ellipse.64x2 + y2 - 640x + 1536 = 0
A. (x - 8)2 + 
= 1
center: (8, 0); foci: (8, 2
), (8, -2
); vertices:(8, 5), (8, -5)
B. 
+ (y - 8)2 = 1
center: (8, 0); foci: (8, 2
), (8, -3
); vertices:(8, 5),
(8, -5)
C. 
+ (y - 5)2 = 1
center: (5, 0); foci: (5, 3
), (5, -3
); vertices:(5, 8), (5, -8)
D. (x - 5)2 + 
= 1
center: (5, 0); foci: (5, 3
), (5, -3
); vertices:(5, 8), (5, -8)
Divide.
÷ 
A. 
B. 5x2 + 5x
C. 
D. 5x2
Which equation matches the given calculator-generated graph and description? Decide without using your calculator.
Parabola; opens left
A. y = -x2 B. x = y2 C. y = x2 D. x = -y2
Differentiate.