Question

15 stacy and stephanie are building a 4 - level square pyramid out of wooden blocks. each of the levels of the pyramid consists of a consecutive perfect square amount of blocks with the top level having 4 blocks. if they decided to add a fifth level, how many blocks would be in the bottom level?
a. 25
b. 36
c. 49
d. 64

1. considering the arithmetic sequence: $11\frac{1}{2}, 9\frac{5}{16}, 7\frac{1}{8}, \dots$

what is the common difference between each term?
a. $-2\frac{3}{16}$
b. 2
c. $\frac{3}{16}$
d. $-\frac{3}{16}$

Explanation:

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Question 15

Step1: Identify top level value

Top level: $4 = 2^2$

Step2: List levels' square terms

Level 1: $2^2$, Level 2: $3^2$, Level 3: $4^2$, Level 4: $5^2$

Step3: Find 5th level term

5th level: $(2+4)^2 = 6^2 = 36$

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Question 16

Step1: Convert terms to improper fractions

$11\frac{1}{2} = \frac{23}{2} = \frac{184}{16}$, $9\frac{5}{16} = \frac{149}{16}$

Step2: Calculate common difference

$\text{Common difference} = \frac{149}{16} - \frac{184}{16} = -\frac{35}{16} = -2\frac{3}{16}$

Answer:

1. B. 36
2. A. $-2\frac{3}{16}$