19) The sum of the <em>arithmetic</em> series is - 397. (Correct choice: E)
33) The sum of the <em>geometric</em> series is 1700. (Correct choice: E)
<h3>How to determine the sum of a given series</h3>
19) <em>Arithmetic</em> series are sets of elements generated by a <em>linear</em> expression of the form:
aₙ = a₁ + (n - 1) · d (1)
Where:
- aₙ - n-th term of the series
- a₁ - First term of the series
- n - Index of the n-th term of the series.
- d - Change between two consecutive elements of the series.
If we know that a₁ = 27, n = 20 and d = - 5, then sum of the first 20 terms of the series is:
x = 27 + 22 + 17 + 12 + 7 + 2 + (- 3) + (- 8) + (- 13) + (- 18) + (- 23) + (- 28) + (- 33) + (- 38) + (- 43) + (- 48) + (- 53) + (- 58) + (- 63) + (- 68)
x = - 397
The sum of the <em>arithmetic</em> series is - 397. (Correct choice: E)
33) <em>Geometric</em> series are sets of elements generated by a <em>exponential</em> expression of the form:
aₙ = a₁ · rⁿ (2)
Where:
- aₙ - n-th term of the series
- a₁ - First term of the series
- r - Ratio between two consecutive elements of the series.
If we know that a₁ = 1458 and r = 1 / 3, then the sum of the first 6 terms of the geometric series is:
x = 1458 + 162 + 54 + 18 + 6 + 2
x = 1700
The sum of the <em>geometric</em> series is 1700. (Correct choice: E)
To learn more on geometric series: brainly.com/question/4617980
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Answer:
C XD
Step-by-step explanation:
The altitude of a triangle goes from the vertex (corner) to the opposite side. It must be perpendicular to the opposite side ( at a right angle)
XD is an altitude
Answer: Shortest side = 6 inches, Medium side = 10 inches and Longest side = 11 inches
Step-by-step explanation: The perimeter has been given as 27 inches, and we know that the perimeter of any given figure is the addition of all sides. The sides are unknown yet, but we have clues as follows;
The longest side is 5 inches longer than the shortest side, hence the longest side equals s + 5. The medium side is 4 inches longer than the shortest side, hence the medium side equals s+ 4. Th shortest side remains s.
Therefore with the perimeter given as 27, we now have the expression;
s + s + 4 + s + 5 = 27
3s + 9 = 27
Subtract 9 from both sides of the equation
3s = 18
Divide both sides of the equation by 3
s = 6
Hence, the sides of the triangle are given as 6, (6+ 4) and (6+ 5), which is,
6 inches, 10 inches and 11 inches.
Answer:
14.2
Step-by-step explanation: