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Let r be any real number such that |r| < 1 and let a = 6 - 6r.Then the geometric sequence: a, ar, ar^2, ar^3, ... will converge to 6.Since the choice of r is arbitrary within the given range, there are infinitely many possible answers.
A geometric sequence is a sequence where each term is a constant multiple of the preceding term. This constant multiplying factor is called the common ratio and may have any real value. If the common ratio is greater than 0 but less than 1 then this produces a descending geometric sequence. EXAMPLE : Consider the sequence : 12, 6, 3, 1.5, 0.75, 0.375,...... Each term is half the preceding term. The common ratio is therefore ½ The sequence can be written 12, 12(½), 12(½)2, 12(½)3, 12(½)4, 12(½)5,.....
Your age on January 1 each year. Or, the year number on January 1 each year.
y = a*r^n where a and r are non-zero constants, and n is a counter.