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Tpy6a [65]
3 years ago
15

What is the twentieth term of the arithmetic sequence described by the equation an= 3n - 10?

Mathematics
1 answer:
sergij07 [2.7K]3 years ago
8 0

Answer:

The twentieth term is 50.

Step-by-step explanation:

The equation that describes the arithmetic sequence describes it's "general term", which means that all the numbers in that sequence must follow that equation. For instance, if we want to find the first term of the sequence we must make a = 1 and we have:

a1 = 3*1 - 10

a1 = -7

Therefore to find the twentieth term we need to make n equal to 20. This is done below:

a20 = 3*20 - 10

a20 = 60 - 10

a20 = 50

The twentieth term is 50.

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Factorise each of the following algebraic expressions completely,
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Answer:

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Step-by-step explanation:

(a)

Given

2k - 6k² + 4k³ ← factor out 2k from each term

= 2k(1 - 3k + 2k²)

To factor the quadratic

Consider the factors of the product of the constant term ( 1) and the coefficient of the k² term (+ 2) which sum to give the coefficient of the k- term (- 3)

The factors are - 1 and - 2

Use these factors to split the k- term

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1(1 - k) - 2k(1 - k) ← factor out (1 - k) from each term

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1 - 3k + 2k² = (1 - k)(1 - 2k) and

2k - 6k² + 4k³ = 2k(1 - k)(1 - 2k)

(b)

Given

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3 years ago
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Step-by-step explanation:

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Write an equation of the line that passes through (3,1) and (0,10) .
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Step-by-step explanation:

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2 years ago
Find the midpoint of the line segment JK if j (4,6) and k(0,-4)
Snowcat [4.5K]

Answer:

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General Formulas and Concepts:

Order of Operations: BPEMDAS

Midpoint Formula: (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

Step-by-step explanation:

<u>Step 1: Define points</u>

J (4, 6)

K (0, -4)

<u>Step 2: Find midpoint</u>

  1. Substitute:                         (\frac{4+0}{2},\frac{6-4}{2})
  2. Add/Subtract:                    (\frac{4}{2},\frac{2}{2})
  3. Divide:                               (2,1)
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