Final Exam S1 (IBMath SL- Yr1) Arithmetic & Geometric Sequences

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Mathematics
•
9th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an arithmetic sequence?
Back
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.
2.
FLASHCARD QUESTION
Front
How do you find the nth term of an arithmetic sequence?
Back
The nth term of an arithmetic sequence can be found using the formula: \( a_n = a_1 + (n-1)d \), where \( a_1 \) is the first term and \( d \) is the common difference.
3.
FLASHCARD QUESTION
Front
What is a geometric sequence?
Back
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
4.
FLASHCARD QUESTION
Front
How do you find the nth term of a geometric sequence?
Back
The nth term of a geometric sequence can be found using the formula: \( a_n = a_1 \cdot r^{(n-1)} \), where \( a_1 \) is the first term and \( r \) is the common ratio.
5.
FLASHCARD QUESTION
Front
What is the formula for the sum of the first n terms of an arithmetic sequence?
Back
The sum of the first n terms of an arithmetic sequence can be calculated using the formula: \( S_n = \frac{n}{2} (a_1 + a_n) \) or \( S_n = \frac{n}{2} (2a_1 + (n-1)d) \).
6.
FLASHCARD QUESTION
Front
What is the formula for the sum of the first n terms of a geometric sequence?
Back
The sum of the first n terms of a geometric sequence can be calculated using the formula: \( S_n = a_1 \frac{1 - r^n}{1 - r} \) (for \( r \neq 1 \)).
7.
FLASHCARD QUESTION
Front
How do you determine if a sequence is arithmetic or geometric?
Back
To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant. To determine if it is geometric, check if the ratio of consecutive terms is constant.
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