Find the sum of the first 30 terms of the sequence, An = 3n + 2
Answer:
The sum of the first 30 terms of the sequence [tex]\( A_n = 3n + 2 \)[/tex] is 1455.
Explanation:
To find the sum of the first 30 terms of the sequence [tex]\( A_n = 3n + 2 \),[/tex] we need to substitute the values of [tex]\( n \)[/tex] from 1 to 30 into the formula and then add them together.
The formula for the [tex]\( n \)[/tex]th term of the sequence is [tex]\( A_n = 3n + 2 \).[/tex]
Let's find the first 30 terms of the sequence:
[tex]\[ A_1 = 3(1) + 2 = 5 \][/tex]
[tex]\[ A_2 = 3(2) + 2 = 8 \][/tex]
[tex]\[ A_3 = 3(3) + 2 = 11 \][/tex]
[tex]\[ \vdots \][/tex]
[tex]\[ A_{30} = 3(30) + 2 = 92 \][/tex]
Now, we need to find the sum of these terms:
[tex]\[ \text{Sum} = A_1 + A_2 + A_3 + \ldots + A_{30} \][/tex]
To find the sum, we can use the formula for the sum of an arithmetic series:
[tex]\[ \text{Sum} = \frac{n}{2}(A_1 + A_{30}) \][/tex]
Where:
- [tex]\( n \)[/tex] is the number of terms (30 in this case)
- [tex]\( A_1 \)[/tex] is the first term (5)
- [tex]\( A_{30} \)[/tex] is the 30th term (92)
Now, let's calculate the sum:
[tex]\[ \text{Sum} = \frac{30}{2}(5 + 92) \][/tex]
[tex]\[ \text{Sum} = \frac{30}{2}(97) \][/tex]
[tex]\[ \text{Sum} = 15 \times 97 \][/tex]
[tex]\[ \text{Sum} = 1455 \][/tex]
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What are the real and imaginary parts of the complex number? −6−i Enter your answers in the boxes. The real part: The imaginary part:
Answer:
Real part = -6 and imaginary part = -i
Step-by-step explanation:
A complex number can be written as a + bi,
where both a and b are real numbers,
While, i is an imaginary number ( equals to √-1, because √-1 does not defined as a real number ),
The product of a real number and imaginary number is imaginary number,
∴ bi is called imaginary part of a + bi
Also, a is real number ⇒ a is real part of a + bi
Here, the given complex number,
-6-i
By comparing,
Imaginary part = -i, real part = -6.
We want to see the real and imaginary parts of a given complex number.
The real part is: -6
The imaginary part is: -1
A general complex number is written as:
z = a + b*i
Where a is the real part and b is the imaginary part.
In this case, we have the number:
z = -6 - i
We can rewrite this as:
z = -6 + (-1)*i
Then the real part is the number that is alone, in this case, -6.
The imaginary part is the coefficient that multiplies the "i", which is -1.
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Answer:
15i² + 49i + 33.
Step-by-step explanation:
Given : (8 + 3i)(3 + 5i).
To find : Multiply .
Solution : We have given (8 + 3i)(3 + 5i).
Distribute 8 over (3 + 5i) and 3i over (3 + 5i).
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You have 128 ounces of milk and drink 16 ounces per day. What algebraic expression models the amount of milk you have? Let x equal the amount of days
The algebraic expression that the amount of milk has will be 128 - 16x.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
Given,
Total milk = 128 ounces
Rate of drinking milk = 16 ounces/day
x equal the number of days
Then,
Amount remaining = 128 - 16x
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