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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