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podryga [215]
3 years ago
14

A sequence is shown.

Mathematics
1 answer:
marin [14]3 years ago
6 0

Answer:

Step-by-step explanation:

The given sequence of numbers is increasing in geometric progression. The consecutive terms differ by a common ratio, r

Common ratio = 6/3 = 12/6 = 2

The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = 3

r = 2

The function, f(n), representing the nth term of the sequence is

f(n) = 3 × 2^(n - 1)

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Answer:

D

Step-by-step explanation:

our basic Pythagorean identity is cos²(x) + sin²(x) = 1

we can derive the 2 other using the listed above.

1. (cos²(x) + sin²(x))/cos²(x) = 1/cos²(x)

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2.(cos²(x) + sin²(x))/sin²(x) = 1/sin²(x)

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A. sin^2 theta -1= cos^2 theta

this is false

cos²(x) + sin²(x) = 1

isolating cos²(x)

cos²(x) = 1-sin²(x), not equal to sin²(x)-1

B. Sec^2 theta-tan^2 theta= -1

1 + tan²(x) = sec²(x)

sec²(x)-tan(x) = 1, not -1

false

C. -cos^2 theta-1= sin^2

cos²(x) + sin²(x) = 1

sin²(x) = 1-cos²(x), our 1 is positive not negative, so false

D. Cot^2 theta - csc^2 theta=-1

cot²(x) + 1 = csc²(x)

isolating 1

1 = csc²(x) - cot²(x)

multiplying both sides by -1

-1 = cot²(x) - csc²(x)

TRUE

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