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sergejj [24]
3 years ago
12

the third term of an arithmetic sequence is 24 and the fifth is 32 if the first term is a1. which is an equation nth term of the

sequence
Mathematics
2 answers:
const2013 [10]3 years ago
8 0
An = a1 + (n - 1)(d)
Where a1 is the first term and d is the common difference.
First find d, the common difference.
24, ____, 32
a3 a4 a5
Subtract 32-24 = 8
Subtract a5 - a3 = 2
Divide 8/2 = 4
d = 4
Use d and one of the values they give us to find a1.
a3 = 24
24 = a1 + (3 - 1)(4)
24 = a1 + 2(4)
24 = a1 + 8
Subtract 8 from both sides
16 = a1
an = 16 + (n - 1)(4)
Can also be written
an = 16 + 4n - 4
an = 4n + 12
Fudgin [204]3 years ago
6 0

Answer:

The nth term of the sequence is a_n=4n+12

Step-by-step explanation:

Given: a_3=24,\ \ a_5=32

First term: a_1

Formula:

a_n=a_1+(n-1)d

where, d is common difference

a_3=24

a_1+2d=24

a_1+4d=32

Subtract both equation

2d=32-24

2d=8

d=4

Put d=4 into a_1+2d=24

a_1+2(4)=24

a_1=16

Now, we will find nth term of the sequence.

a_n=16+(n-1)4

a_n=16+4n-4

a_n=4n+12

Hence, The nth term of the sequence is a_n=4n+12

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Pani-rosa [81]

Answer:

a. m<B = 100°

b. m<L = 55°

c. Scale factor = 9/11

Step-by-step explanation:

a) Similar triangles have their three corresponding angles congruent to each other, while the ratio of their corresponding sides are proportional to each other.

Since ∆ABC ~ ∆GLJ, therefore,

<A = <G,

<B = <J

<C = <L

m<J = 100° (given)

Therefore,

m<B = m<J = 100°

m<B = 100°

b) m<A = m<G

m<A = 25° (given)

Therefore,

m<A = m<G = 25°

m<G = 25°

m<L = 180° - (m<J + m<G)

Substitute

m<L = 180° - (100° + 25°)

m<L = 55°

c) scale factor of smaller triangle to the larger = side length of smaller triangle / corresponding side length of bigger triangle

Scale factor = AB/GJ

Substitute

Scale factor = 18/22

Simplify

Scale factor = 9/11

8 0
3 years ago
8-7-6-5-4-3-2-1-0-1-2-3
Sindrei [870]

Answer:

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Step-by-step explanation:

8 0
3 years ago
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What expressions are equivalent to q+p+q+p+q
Kipish [7]
You can resolve all of them.
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6 0
3 years ago
Peter Piper bought 5 pickled pepper plants. Each plant cost $110. He also needed a
marysya [2.9K]

Answer:

6.75

Step-by-step explanation:

10.00-3.25= 5.75

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7 0
3 years ago
The paint mixer wants to mix paint that is 30% gloss with paint that is 15% gloss to make 3.75 gallons of paint that is 20% glos
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The paint mixer should mix 1.238 gallon paint that is 30 % gloss and 2.512 gallon paint that is 15 % gloss to get 3.75 gallon of paint that is 20 % gloss.

In this question we must determine the correct volumes of each paint to obtain a 20 % gloss with paint by means of weighted averages:

c_{r} = x\cdot c_{a} +(1-x)\cdot c_{b} (1)

Where:

  • x - Proportion of the paint that is 30 % gloss.
  • c_{a} - Concentration ratio of the paint that is 30 % gloss.
  • c_{b} - Concentration ratio of the paint that is 15 % gloss.
  • c_{r} - Resulting concentration ratio

If we know that c_{a} = 0.3, c_{b} = 0.15 and c_{r} = 0.2, then the proportion of the paint that is 30 % gloss is:

0.2 = 0.3\cdot x +(1-x)\cdot 0.15

0.2 = 0.15\cdot x+0.15

0.15\cdot x = 0.05

x = 0.33

And the quantity of gallons needed of each paint are:

Paint (30 % gloss)

V_{a} = 0.33\cdot (3.75\,gal)

V_{a} = 1.238\,gal

Paint (15 % gloss)

V_{b} = V-V_{a}

V_{b} = 3.75\,gal-1.238\,gal

V_{b} = 2..512\,gal

The paint mixer should mix 1.238 gallon paint that is 30 % gloss and 2.512 gallon paint that is 15 % gloss to get 3.75 gallon of paint that is 20 % gloss.

To learn more on weighted averages, we kindly invite to check this question: brainly.com/question/18554478

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