Arithmetic Sequences1

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•
Mathematics
•
8th 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
What is the common difference in the sequence 13, 19, 25, ...?
Back
The common difference is 6, calculated as 19 - 13 or 25 - 19.
3.
FLASHCARD QUESTION
Front
How do you find the nth term of an arithmetic sequence?
Back
The nth term can be found using the formula: \( a_n = a_1 + (n-1) \cdot d \), where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.
4.
FLASHCARD QUESTION
Front
What is the 6th term in the arithmetic sequence 13, 19, 25, ...?
Back
The 6th term is 43, calculated as \( 13 + (6-1) \cdot 6 = 43 \).
5.
FLASHCARD QUESTION
Front
What is the next term in the sequence 13, 19, 25, ...?
Back
The next term is 31, calculated as \( 25 + 6 = 31 \).
6.
FLASHCARD QUESTION
Front
If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term?
Back
The 10th term is 32, calculated as \( 5 + (10-1) \cdot 3 = 32 \).
7.
FLASHCARD QUESTION
Front
What is the formula for the sum of the first n terms of an arithmetic sequence?
Back
The sum \( S_n \) of the first n terms can be calculated using the formula: \( S_n = \frac{n}{2} \cdot (a_1 + a_n) \) or \( S_n = \frac{n}{2} \cdot (2a_1 + (n-1)d) \).
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