What is an arithmetic series?
Arithmetic and Geometric Series Practice

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Mathematics
•
10th Grade - University
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
An arithmetic series is the sum of the terms of an arithmetic sequence, where each term after the first is obtained by adding a constant difference to the previous term.
2.
FLASHCARD QUESTION
Front
What is a geometric series?
Back
A geometric series is the sum of the terms of a geometric sequence, where each term after the first is obtained by multiplying the previous term by a constant ratio.
3.
FLASHCARD QUESTION
Front
How do you find the sum of the first n terms of an arithmetic series?
Back
The sum S_n of the first n terms of an arithmetic series can be calculated using the formula: S_n = n/2 * (a + l), where a is the first term, l is the last term, and n is the number of terms.
4.
FLASHCARD QUESTION
Front
How do you find the sum of the first n terms of a geometric series?
Back
The sum S_n of the first n terms of a geometric series can be calculated using the formula: S_n = a * (1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms.
5.
FLASHCARD QUESTION
Front
Evaluate the sum of the geometric series: -1 + 5 - 25 + 125 + ... + 78,125
Back
The sum is 65104.
6.
FLASHCARD QUESTION
Front
Evaluate S_8 for the series: 2 + 6 + 10 + 14 + ...
Back
S_8 = 128.
7.
FLASHCARD QUESTION
Front
Evaluate S_n for the series: 28 + 35 + 42 + 49 + ..., n = 10
Back
S_n = 595.
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