find the 8th term of the geometric sequence and the common ratio whose 1st term is 1/27 and 1/9 is the 2nd term.
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find the 8th term of the geometric sequence and the common ratio whose 1st term is 1/27 and 1/9 is the 2nd term.
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Answer:The two simplest sequences to work with are arithmetic and geometric sequences.
An arithmetic sequence goes from one term to the next by always adding (or subtracting) the same value. For instance, 2, 5, 8, 11, 14,... is arithmetic, because each step adds three; and 7, 3, –1, –5,... is arithmetic, because each step subtracts 4.
The number added (or subtracted) at each stage of an arithmetic sequence is called the "common difference" d, because if you subtract (that is, if you find the difference of) successive terms, you'll always get this common value.
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A geometric sequence goes from one term to the next by always multiplying (or dividing) by the same value. So 1, 2, 4, 8, 16,... is geometric, because each step multiplies by two; and 81, 27, 9, 3, 1, \frac{1}{3}
3
1
,... is geometric, because each step divides by 3.
The number multiplied (or divided) at each stage of a geometric sequence is called the "common ratio" r, because if you divide (that is, if you find the ratio of) successive terms, you'll always get this common value.