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elena-s [515]
2 years ago
15

The fourth term of an Arithmetic Sequence is equal to 3 times the first term, and the seventh term exceeds twice the third term

by 1. find the first term and common difference.​
Mathematics
1 answer:
11Alexandr11 [23.1K]2 years ago
8 0

Answer:

The first term is 3. The common difference is 2.

Step-by-step explanation:

The first term is x.

The common difference is d.

The second term is x + d.

3rd term: x + 2d

4th term: x + 3d

7th term: x + 6d

"The fourth term of an Arithmetic Sequence is equal to 3 times the first term"

x + 3d = 3 * x       Eq. 1

"the seventh term exceeds twice the third term by 1"

x + 6d = 2(x + 2d) + 1       Eq. 2

Simplify Eq. 1:

2x = 3d

Simplify Eq. 2:

x + 6d = 2x + 4d + 1

x = 2d - 1

Multiply both sides of the last equation by 2.

2x = 4d - 2

2x = 3d   (simplified Eq. 1)

Since 2x = 2x, then the right sides are equal.

3d = 4d - 2

d = 2

2x = 3d

2x = 3(2)

2x = 6

x = 3

Answer: The first term is 3. The common difference is 2.

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40x=10x^2+41 <br><br> Identify the number of solutions and their types using the discriminant
nydimaria [60]

Number of solutions: no roots

Type of solution: Not Real

Step-by-step explanation:

We need to identify the number of solutions and their types using the discriminant.

We are given: 40x=10x^2+41\\

Rearranging:

40x-10x^2-41=0\\10x^2-40x+41=0

Discriminant can be found by: b^2-4ac

where b=-40, a=10 and c=41

Putting values:

b^2-4ac\\=(-40)^2-4(10)(41)\\=1600-1640\\=-40\\

So, Discriminant is -40

If the discriminant is less than zero i.e -40 then there are no real roots.

So, Number of solutions: no roots

Type of solution: Not Real

Keywords: discriminant

Learn more about discriminant at:

  • brainly.com/question/8196933
  • brainly.com/question/9328925
  • brainly.com/question/9184197

#learnwithBrainly

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