The 21st term of the given arithmetic sequence is 83. The nth term of an arithmetic sequence is applied to find the required value where n = 21.
<h3>What is the nth term of an arithmetic series?</h3>
The nth term of an arithmetic sequence is calculated by the formula
aₙ = a + (n - 1) · d
Here the first term is 'a' and the common difference is 'd'.
<h3>Calculation:</h3>
The given sequence is an arithmetic sequence.
3, 7, 11, 15, 19, ....
So, the first term in the sequence is a = 3 and the common difference between the terms of the given sequence is d = 7 - 3 = 4.
Thus, the required 21st term in the sequence is
a₂₁ = 3 + (21 - 1) × 4
⇒ a₂₁ = 3 + 20 × 4
⇒ a₂₁ = 3 + 80
∴ a₂₁ = 83
So, the 21st term in the given arithmetic sequence is 83.
Learn more about the arithmetic sequence here:
brainly.com/question/6561461
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On the complex plane, the real component of a complex number is graphed along the horizontal axis while the imaginary component is graphed along the vertical axis.
Positive numbers go to the right on the real axis and up on the imaginary axis, and vice versa for negative numbers.
Therefore, the number -14-5i is in the 3rd quadrant because it graphed to the left of the origin and down.
Division yields
Now for partial fractions: you're looking for constants <em>a</em>, <em>b</em>, and <em>c</em> such that
which gives <em>a</em> + <em>b</em> = 2, <em>c</em> = 0, and 2<em>a</em> = -7, so that <em>a</em> = -7/2 and <em>b</em> = 11/2. Then
Now, in the integral we get
The first two terms are trivial to integrate. For the third, substitute <em>y</em> = <em>x</em> ² + 2 and d<em>y</em> = 2<em>x</em> d<em>x</em> to get
Answer:
I got x = 1
Step-by-step explanation:
First to isolate the variable you add 3 to both sides which will give you 1/2x is less than or equal to 2. Then divide both sides by 1/2 and you will get x = 1. To check the answer I just did:
And since -2.5 is less than -1 this statement is true. x does in fact equal 1
Answer:
See below ~
Step-by-step explanation:
<u>P (6th grader)</u>
- No. of 6th graders / Total students
- 6 / 6 + 7 + 8
- 6/21
- 2/7
<u>P (6th grader after)</u>
- No. of 6th graders - 1 / Total students - 1
- 6 - 1 / 21 - 1
- 5/20
- 1/4
<u>Question 1 : P (Both 6th graders)</u>
- P = P (6th grader) × P (6th grader after)
- P = 2/7 x 1/4 = 2/28 = <u>1/14</u>
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<u>Question 2 : P' (Both 6th graders)</u>
- P' = 1 - P
- P' = 1 - 1/14
- P' = <u>13/14</u>