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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Answer:
The equation to determine the total length in kilometers is 
The total length in kilometers of Josh’s hike is 38 km.
Step-by-step explanation:
Given:
Let the total length in kilometers of Josh’s hike be h.
Now Given that He has now hiked a total of 17 km and is 2 km short of being 1/2 of the way done with his hike.
It means that to reach half of the length of total length Josh needs 2 more km to add in his hiking which is done which is of 17 km.
Framing the above sentence in equation form we get;
Hence, The equation to determine the total length in kilometers is
Now Solving the above equation we get;
First we will multiply 2 on both side using Multiplication property we get;
Hence, The total length in kilometers of Josh’s hike is 38 km.
Answer:
In geometry, a transformation is an operation that moves, flips, or changes a shape (called the preimage) to create a
new shape (called the image). A translation is a type of transformation that moves each point in a figure the same
distance in the same direction. Translations are often referred to as slides. You can describe a translation using words
like "moved up 3 and over 5 to the left" or with notation. There are two types of notation to know.
1. One notation looks like T(3, 5). This notation tells you to add 3 to the x values and add 5 to the y values.
2. The second notation is a mapping rule of the form (x, y) → (x−7, y+5). This notation tells you that the x and
y coordinates are translated to x−7 and y+5.
Step-by-step explanation:
