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Arithmetic and geometric sequences
Arithmetic sequences
An arithmetic sequence is a sequence of numbers each of which, after the first, is obtained by adding to the preceding number a constant number called the common difference.

Thus, 3, 8, 13, 8, 23,... is an arithmetic sequence because each term is obtained by adding 5 to the preceding number.

If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then:
a2=a1+d
a3=a2+d=a1+2d
a4=a3+d=a1+3d

an=a1+(n-1)d

To solve exercises using aritmetic sequences you need the following formulas:
• The nth term: an= a1+ (n-1) d
where:
a1 = the first term of the sequence
d = common difference (Remember you can obtain it using d=an-an-1 or .)
n = number of terms
an = nth term

Given the arithmetic sequence 11, 7, 3,... Find the 301st term, a301
an= a1+ (n-1) d
a301= 11+ (300-1)·(-4)=-1189

 Compute the 20 (th) term of the arithmetic sequence where a 4 = -19 and d=-4

Solution =