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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.

Basic Concepts:Pascal's triangle, Binomial theorem, Introduction to sequences, Monotonic and bounded sequences,

• arithmetic sequence: a sequence with a common difference between successive terms

• The nth term, ${t_n}$ ,of an arithmetic sequence:

${t_n} = {t_1} + \left( {n - 1} \right)d$

where, ${t_n}$: nth term

${t_1}$: first term

$d$ : common difference

• The nth term, ${t_n}$ ,of an arithmetic sequence:

${t_n} = {t_1} + \left( {n - 1} \right)d$

where, ${t_n}$: nth term

${t_1}$: 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 $t_1,d,t_n$ for the sequences in which two terms are givena)$t_4=14$, $t_{10}=32$b)$t_3=-14$, $t_{12}=-59$
- 3.Three consecutive terms of an arithmetic sequence are written in the form:

$1+2x,7x,3+4x$

Solve for the value of x.

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