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:
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Answer:
408
Step-by-step explanation:
You would set up a proportion of 1/12 = 34/x. You would do the butterfly method and get 1x=408. Then divide 408 by 1 to get 408.
Answer:
-1/6
Step-by-step explanation:
= 1/3 (-1-1) x -1/4 (-1)
= 1/3 (-2) x 1/4
= -2/3 x 1/4
= -2\12
2 and 12 can cancel out each other.
so the answer will be.
= -1/6.
all of those r correct :)
Step-by-step explanation:
The equation of a parabola with focus at (h, k) and the directrix y = p is given by the following formula:
(y - k)^2 = 4 * f * (x - h)
In this case, the focus is at the origin (0, 0) and the directrix is the line y = -1.3, so the equation representing the cross section of the reflector is:
y^2 = 4 * f * x
= 4 * (-1.3) * x
= -5.2x
The depth of the reflector is the distance from the vertex to the directrix. In this case, the vertex is at the origin, so the depth is simply the distance from the origin to the line y = -1.3. Since the directrix is a horizontal line, this distance is simply the absolute value of the y-coordinate of the line, which is 1.3 inches. Therefore, the depth of the reflector is approximately 1.3 inches.
