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allochka39001 [22]
3 years ago
7

Find the first five terms of the sequence in which a1 = 6 and an = –3an – 1 – 12, if n ≥ 2.

Mathematics
1 answer:
KatRina [158]3 years ago
8 0

Answer:

\huge\boxed{6,\ -30;\ 78;\ -246;\ 690}

Step-by-step explanation:

a_1=6\\a_n=-3a_{n-1}-12\qquad n\geq2\\\\\text{Substitute}\ n=2,\ n=3,\ n=4,\ n=5\ \text{to}\ a_n=-3a_{n-1}-12:\\\\\text{for}\ n=2\\\\a_2=-3a_{2-1}-12=-3a_1-12\\\\\text{substitute}\ a_1=6\\\\a_2=-3(6)-12=-18-12=-30\\\\\text{for}\ n=3\\\\a_3=-3a_{3-1}-12=-3a_2-12\\\\\text{substitute}\ a_2=-30\\\\a_3=-3(-30)-12=90-12=78

\text{for}\ n=4\\\\a_4=-3a_{4-1}-12=-3a_3-12\\\\\text{substitute}\ a_3=78\\\\a_4=-3(78)-12=-234-12=-246\\\\\text{for}\ n=5\\\\a_5=-3a_{5-1}-12=-3a_4-12\\\\\text{substitute}\ a_4=-246\\\\a_5=-3(-246)-12=702-12=690

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Step-by-step explanation:

5 0
3 years ago
What is the equation of a line, in point- slope form, that passes through (5, -3) and has a slope of 2/3?
Alika [10]
<h3><u><em>Option B</em></u></h3><h3><u><em>The equation of a line, in point- slope form, that passes through (5, -3) and has a slope of 2/3</em></u></h3><h3><u><em /></u>y + 3 = \frac{2}{3}(x -5)<u><em /></u></h3>

<em><u>Solution:</u></em>

<em><u>The equation of line in point slope form is given as:</u></em>

y - y_1 = m(x-x_1)

Where, "m" is the slope of line

Given that,

slope = 2/3

m = \frac{2}{3}

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Substitute m = 2/3 and (x_1, y_1) = (5, -3) in point slope form

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8 0
3 years ago
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Reil [10]
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3 0
3 years ago
Read 2 more answers
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Answer:

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Step-by-step explanation:

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Now you add the 1.8 to 2 and get 3.8

Now for the equation you just need to plug in what you did so...

(0.3 X 6) + (0.40 X 5) =  3.8

Glad i could help :)

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3 years ago
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nlexa [21]

Answer:

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Step-by-step explanation:

5 0
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