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Arithmetic sequences
- Lesson: 1a3:09
- Lesson: 1b3:01
- Lesson: 1c7:05
- Lesson: 2a4:24
- Lesson: 2b5:46
- Lesson: 35:27
Arithmetic sequences
An arithmetic sequence (arithmetic progression) is a number sequence with a common difference between successive terms. By using the arithmetic sequence formula, we can easily find the value of a term and the common difference in the sequence.
Related Concepts: Pascal's triangle, Binomial theorem, Introduction to sequences, Monotonic and bounded sequences
Lessons
• arithmetic sequence: a sequence with a common difference between successive terms
• The nth term, tn ,of an arithmetic sequence:
tn=t1+(n−1)d
where, tn: nth term
t1: first term
d : common difference
• The nth term, tn ,of an arithmetic sequence:
tn=t1+(n−1)d
where, tn: nth term
t1: first term
d : common difference
- 1.Arithmetic sequence formula
Consider the arithmetic sequence: 5, 9, 13, 17, … .a)Identify the common difference.b)Determine the seventh term of the sequence.c)Which term in the sequence has a value of 85? - 2.Determine t1,d,tn for the sequences in which two terms are givena)t4=14, t10=32b)t3=−14, t12=−59
- 3.Three consecutive terms of an arithmetic sequence are written in the form:
1+2x,7x,3+4x
Solve for the value of x.