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.
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.
Arithmetic series is the indicated sum of the terms of an arithmetic sequence.
The sequence 5, 11, 17, 23, 29, 35 is an arithmetic sequence.
5 + 11 + 17 + 23 + 29 + 35 is the corresponding arithmetic series.
Find the next four terms of the given arithmetic sequence. 7, 4, 1, - 2, - 5 . . .
A. - 3, - 3, - 3, - 3
B. - 8, -5, -2, 1
C. - 8, - 11, - 14, - 17
D. 8, 11, 14, 17
Correct Answer: C
Step 1: The common difference for the given sequence is - 3.
Step 2: So, the next four terms are - 8, - 11, - 14, - 17.
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.
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.