12 Questions
What is a number sequence?
A set of numbers written according to a particular rule
Define an arithmetic sequence.
A sequence where each term is obtained by adding a fixed number to the previous term.
How can the difference between any two terms of an arithmetic sequence be calculated?
The difference is the product of the difference of positions and the common difference.
What remains the same for each term of an arithmetic sequence when divided by the common difference?
The remainder
What is the algebraic form of an arithmetic sequence with the first term f and common difference d?
$x_n = dn + (f - d)$
How can the number of terms in an arithmetic sequence be calculated?
$n = \frac{x_n - x_1}{d} + 1$
Define an arithmetic sequence with a first term of 7 and a common difference of 3.
7, 10, 13, 16, ...
What is the 11th term of the arithmetic sequence with a first term of 7 and a common difference of 3?
37
What are the first term and the common difference of the arithmetic sequence defined by the algebraic expression 5n+2?
First term: 7, Common difference: 5
Is 123 a term of the arithmetic sequence 3, 6, 9, ...? Why?
No, 123 is not a term of the sequence.
Calculate the difference between the sums of the first 20 terms of the sequences 5, 9, 13, ... and 10, 14, 18, ...
160
What is the common difference of the arithmetic sequence 4, 9, 14, ...? What is the difference between its 5th and 25th terms?
Common difference: 5, Difference: 100
Explore the concept of number sequences, including multiples, squares of natural numbers, and prime numbers. Learn about arithmetic sequences, where a fixed number is added repeatedly, known as the common difference.
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