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:
1941.2 feet
Step-by-step explanation:
Answer:
It looks like you cut off part of the questions...
Step-by-step explanation:
Answer:
Neither
Step-by-step explanation:
Since we only know the measure of the angles, we can only say the triangles are similar, not congruent. We need at least one side measurement on each triangle to determine if the triangles are congruent. And it would have to be the same side measurement. Then we could use ASA (Angle side Angle) or AAS ( Angle Angle side) to determine congruence.
The triangles are similar
62+39 +79 = 180
The three angles are the same
<A = 62 = <X = 62
<B = 39 = <Y = 39
<C = 79 = <Z = 79
This is shown by AAA similarity
