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Cloud [144]
3 years ago
13

Let the sequence {an} be defined so that a1 = 1 and each succeeding term is found by adding 3 to the one before it. Find the for

mula representing an, the nth term of the sequence.
A) n - 2
B) n + 3
C) 3n - 2
D) 3n + 3
Mathematics
1 answer:
Sauron [17]3 years ago
6 0

Answer:

C

Step-by-step explanation:

The sequence is arithmetic with n th term

a_n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 1 and d = 3, thus

a_{n} = 1 + 3(n - 1) = 1 + 3n - 3 = 3n - 2 → C

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SashulF [63]

Answer:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

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And the anfle is approximately \theta \approx 48

Step-by-step explanation:

For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

a=[1,2,-2], b=[4,0,-3,]

The dot product on this case is:

a b= (1)*(4) + (2)*(0)+ (-2)*(-3)=10

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

|a|= \sqrt{(1)^2 +(2)^2 +(-2)^2}=\sqrt{9} =3

|b| =\sqrt{(4)^2 +(0)^2 +(-3)^2}=\sqrt{25}= 5

And finally we can calculate the angle between the vectors like this:

cos \theta = \frac{ab}{|a| |b|}

And the angle is given by:

\theta = cos^{-1} (\frac{ab}{|a| |b|})

If we replace we got:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately \theta \approx 48

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3 years ago
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