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Nikolay [14]
2 years ago
14

Write a rule for the nth term of the arithmetic sequence described below.

Mathematics
1 answer:
belka [17]2 years ago
7 0

Answer:

an = 115 + (n - 1) (-6)

a25 = - 29

Step-by-step explanation:

We use the definition for the nth term of an arithmetic sequence:

an = a1 + (n - 1) d

a5 = 91 = a1 + (5 - 1) d

91 = a1 + 4 d

a20 = 1 = a1 + (20 - 1) d = a1 + 19 d

1 = a1 + 19 d

now we subtract term by term one expression from the other

90 = 4 d - 19 d

90 = - 15 d

divide both sides by -15 to isolate d

d = 90 / (-15) = -6

Now we can calculate what a1 is using for example:

1 = a1 + 19 d

1 = a1 - 114

add 114 to both sides:

115 = a1

Then our general expression for the sequence is:

an = 115 + (n - 1) (-6)

We can now use it to calculate the value of a25:

a25 = 115 + (24) * (-6) = -29

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Answer:2/3

Step-by-step explanation:

Simplifying

(9m + -6) * 7 = 0

Reorder the terms:

(-6 + 9m) * 7 = 0

Reorder the terms for easier multiplication:

7(-6 + 9m) = 0

(-6 * 7 + 9m * 7) = 0

(-42 + 63m) = 0

Solving

-42 + 63m = 0

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '42' to each side of the equation.

-42 + 42 + 63m = 0 + 42

Combine like terms: -42 + 42 = 0

0 + 63m = 0 + 42

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Divide each side by '63'.

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Simplifying

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7 0
3 years ago
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Question 2:

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Answer:

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