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 5, 8, 11, 14, ...?
Back
The common difference is 3, as each term increases by 3.
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 and \( d \) is the common difference.
4.
FLASHCARD QUESTION
Front
What is the 4th term in the arithmetic sequence 2, 6, 10, ...?
Back
The 4th term is 14.
5.
FLASHCARD QUESTION
Front
If the first term of an arithmetic sequence is 7 and the common difference is 2, what is the 10th term?
Back
The 10th term is 25.
6.
FLASHCARD QUESTION
Front
What is the formula to calculate the sum of the first n terms of an arithmetic sequence?
Back
The sum of the first n terms is given by: \( S_n = \frac{n}{2} \cdot (a_1 + a_n) \) or \( S_n = \frac{n}{2} \cdot (2a_1 + (n-1)d) \).
7.
FLASHCARD QUESTION
Front
What is the next number in the arithmetic sequence 13, 19, 25, ...?
Back
The next number is 31.
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