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ARITHMETIC SEQUENCE

Arithmetic Sequence

Definition Of Arithmetic Sequence

Arithmetic sequence is a sequence of numbers that has a constant difference between every two consecutive terms.

In other words, arithmetic sequence is a sequence of numbers in which each term except the first term is the result of adding the same number, called the common difference, to the preceding term.

Examples of Arithmetic Sequence

The sequence 5, 11, 17, 23, 29, 35 . . . is an arithmetic sequence, because the same number 6 (i.e. the common difference) is added to each term of the sequence to get the succeeding term.

More About Arithmetic Sequence

Arithmetic series is the indicated sum of the terms of an arithmetic sequence.

Video Examples: Arithmetic Sequence

Example of Arithmetic Series

The sequence 5, 11, 17, 23, 29, 35 is an arithmetic sequence.
5 + 11 + 17 + 23 + 29 + 35 is the corresponding arithmetic series.

Solved Example on Arithmetic Sequence

Ques:

Find the next four terms of the given arithmetic sequence. 7, 4, 1, - 2, - 5 . . .

Choices:

A. - 3, - 3, - 3, - 3
B. - 8, -5, -2, 1
C. - 8, - 11, - 14, - 17
D. 8, 11, 14, 17
Correct Answer: C

Solution:

Step 1: The common difference for the given sequence is - 3.
Step 2: So, the next four terms are - 8, - 11, - 14, - 17.

 

Quick Summary

  • Constant difference between consecutive terms
  • General form: a, a+d, a+2d, a+3d, ...
  • d is the common difference
\[ a_n = a_1 + (n-1)d \]

🍎 Teacher Insights

Use real-world examples to illustrate arithmetic sequences (e.g., seating arrangements, salary increases).

🎓 Prerequisites

  • Basic Algebra
  • Number Patterns

Check Your Knowledge

Q1: What is the common difference of the sequence 2, 5, 8, 11...?

Q2: Find the 5th term of the arithmetic sequence with a first term of 3 and a common difference of 2.

Frequently Asked Questions

Q: How do you find the common difference?
A: Subtract any term from its succeeding term.

Q: What is the formula for the nth term?
A: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

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