The sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5
Given,
18th term of an arithmetic sequence = 8.1
Common difference = d = 0.25.
<h3>What is an arithmetic sequence?</h3>
The sequence in which the difference between the consecutive term is constant.
The nth term is denoted by:
a_n = a + ( n - 1 ) d
The sum of an arithmetic sequence:
S_n = n/2 [ 2a + ( n - 1 ) d ]
Find the 18th term of the sequence.
18th term = 8.1
d = 0.25
8.1 = a + ( 18 - 1 ) 0.25
8.1 = a + 17 x 0.25
8.1 = a + 4.25
a = 8.1 - 4.25
a = 3.85
Find the sum of 20 terms.
S_20 = 20 / 2 [ 2 x 3.85 + ( 20 - 1 ) 0.25 ]
= 10 [ 7.7 + 19 x 0.25 ]
= 10 [ 7.7 + 4.75 ]
= 10 x 12.45
= 124.5
Thus the sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5
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Y=x+4
x=0 y=4
x=1 y=5
x=2 y=6
x=3 y=7
plot the points at
(0,4) (1,5) (2,6) and (3,7)
Answer:
12 prob
Step-by-step explanation:
Answer:
<h2>7</h2>
Step-by-step explanation:
![\left[\left(11\:-\:4\right)^3\right]^2\:\div \left(4\:+\:3\right)^5\\\\\frac{\left(\left(11-4\right)^3\right)^2}{\left(4+3\right)^5}\\\\\mathrm{Subtract\:the\:numbers:}\:11-4=7\\\\=\frac{\left(7^3\right)^2}{\left(4+3\right)^5}\\\\\mathrm{Add\:the\:numbers:}\:4+3=7\\\\=\frac{\left(7^3\right)^2}{7^5}\\\\\left(7^3\right)^2=7^6\\\\=\frac{7^6}{7^5}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\\frac{7^6}{7^5}=7^{6-5}\\\\\mathrm{Subtract\:the\:numbers:}\:6-5=1\\\\=7](https://tex.z-dn.net/?f=%5Cleft%5B%5Cleft%2811%5C%3A-%5C%3A4%5Cright%29%5E3%5Cright%5D%5E2%5C%3A%5Cdiv%20%5Cleft%284%5C%3A%2B%5C%3A3%5Cright%29%5E5%5C%5C%5C%5C%5Cfrac%7B%5Cleft%28%5Cleft%2811-4%5Cright%29%5E3%5Cright%29%5E2%7D%7B%5Cleft%284%2B3%5Cright%29%5E5%7D%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A11-4%3D7%5C%5C%5C%5C%3D%5Cfrac%7B%5Cleft%287%5E3%5Cright%29%5E2%7D%7B%5Cleft%284%2B3%5Cright%29%5E5%7D%5C%5C%5C%5C%5Cmathrm%7BAdd%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A4%2B3%3D7%5C%5C%5C%5C%3D%5Cfrac%7B%5Cleft%287%5E3%5Cright%29%5E2%7D%7B7%5E5%7D%5C%5C%5C%5C%5Cleft%287%5E3%5Cright%29%5E2%3D7%5E6%5C%5C%5C%5C%3D%5Cfrac%7B7%5E6%7D%7B7%5E5%7D%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5Cfrac%7Bx%5Ea%7D%7Bx%5Eb%7D%3Dx%5E%7Ba-b%7D%5C%5C%5C%5C%5Cfrac%7B7%5E6%7D%7B7%5E5%7D%3D7%5E%7B6-5%7D%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A6-5%3D1%5C%5C%5C%5C%3D7)
Probabilities are used to determine the likelihood of events
The value of the probability P(thinking of a song)P(turn on the radio and hear the song) is 0.056
<h3>How to estimate the probability</h3>
To calculate the probability, we make use of the following representations:
- Event A represents the likelihood of thinking of a song
- Event B represents the likelihood of turning on the radio and hearing the song
So, we have:
P(thinking of a song)P(turn on the radio and hear the song) = P(A) * P(B)
Assume that:
P(A) = 0.12 and P(B) = 0.47
So, we have:
P(thinking of a song)P(turn on the radio and hear the song) = 0.12* 0.47
Evaluate the product
P(thinking of a song)P(turn on the radio and hear the song) = 0.0564
Approximate
P(thinking of a song)P(turn on the radio and hear the song) = 0.056
Hence, the value of the probability P(thinking of a song)P(turn on the radio and hear the song) is 0.056
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