14. Orlando is making a design for a logo. He begins with a square measuring 20 inches on a side. The second square has a side length of 16 inches, and the third square has a side length of

Question

12.8 inches. Which square will be the first square with a side length of less than 8 inches?
A)seventh square
B) fourth square
C) fifth square
D) sixth square

15. What is the 50th term of the sequence that begins -2, 4, 10, 16
290
294
292
296
16. What is the 20th term of the sequence that begins -3, 6, -12, 24
-524,288
524, 288
1,572, 864
3,145,728

17. The 5th term ina geometric sequence is 160. The 7th is 40. Whar are the possible value of the 6th term of the sequence?
±70
70
±80
80

18. Find the sum of the following series
15∑n=1 (2n+1)
240
255
210
510

Answer 1

Answer:

14. D) sixth square.

To find the side length of the sixth square:

Let x be the side length of the sixth square.

The side length of each square is obtained by multiplying the side length of the previous square by 0.8.

So, we can write:

20 x 0.8^5 = x

x = 7.8125

Therefore, the sixth square has a side length of approximately 7.81 inches, which is less than 8 inches.

15. 296

The sequence is increasing by 6, 6, and 6 for each term. So, the 50th term would be:

-2 + (50-1)6 = 296

16. 1,572,864

The sequence is doubling for each term but with alternating signs. So, the 20th term would be:

-3 x 2^(20-1) = -3 x 524,288 = -1,572,864

17. ±80

We can use the formula for the nth term of a geometric sequence:

an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.

From the given information, we can write:

a5 = 160 = a1 * r^(5-1)

a7 = 40 = a1 * r^(7-1)

Dividing the second equation by the first, we get:

40/160 = (a1 * r^(7-1))/(a1 * r^(5-1))

1/4 = r^2

r = ±√(1/4) = ±1/2

Substituting this value of r in the first equation, we get:

160 = a1 * (1/2)^4

a1 = 160 x 16 = 2560

So, the sixth term would be:

a6 = a1 * r^(6-1) = 2560 x (1/2)^5 = 80 or -80

18. 510

To find the sum of the series:

15∑n=1 (2n+1) = 15(1 + 3 + 5 + ... + 39)

This is an arithmetic series with a common difference of 2.

The formula for the sum of an arithmetic series is:

Sn = n/2(a1 + an), where n is the number of terms, a1 is the first term, and an is the nth term.

In this case, we have:

a1 = 1

an = 39

n = (an - a1)/d + 1, where d is the common difference.

n = (39 - 1)/2 + 1 = 20

So, the sum of the series is:

S20 = 20/2(1 + 39) = 510.