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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
Learn more about arithmetic sequence here:
brainly.com/question/25749583
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I believe it’s the first one. i’m very sorry if it’s wrong
Answer: X= 6 or X=-4
Step-by-step explanation:
Answer:
Maggie spent =30
Karen spent = 10
Jasmine spent =20
Step-by-step explanation:
In this we use algebra to solve.we give the sisters unknowns, to help us solve the equation.
we dont know how much jasmine used so we give her the unknown x.you can use any letter but ill us x.
karen used half as much as karen so we give her 1/2x because it was half of jasmine.maggie used 3 times that of karen so w give her 3(1/2x).
maggie =3(1/2x)
Karen =1/2x
jasmine =x
3(1/2x) + 1/2x + x = 60
3/2x + 1/2x + x = 60
2x + x = 60
3x=60
x=20
where we have x =we replace with 20
e.g karen 1/2x => 1/2 x 20 =10
if you need any clarifications please do tell me in the comment section.i would like to help more if you need help.thx
Hope this helps and if it does mark as branliest anwer thx
