標題:
Math(summation of a geometric sequence)
發問:
1.For each of the following geometric sequences,find the numver of terms n and the sum of the first n terms S(n).(a)1458,486,162,54,...,22.Find the sum of the 4th term to the 10th term of the geometric sequence 2,4,8,16,... .3.The 1st term of a geometric sequence is 1/3 and the 4th term is -1/81.(a)Find the... 顯示更多 1.For each of the following geometric sequences,find the numver of terms n and the sum of the first n terms S(n). (a)1458,486,162,54,...,2 2.Find the sum of the 4th term to the 10th term of the geometric sequence 2,4,8,16,... . 3.The 1st term of a geometric sequence is 1/3 and the 4th term is -1/81. (a)Find the common ratio of the geometric sequence. (b)Hence find the sum of the first 6 terms.
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1.For each of the following geometric sequences,find the numver of terms n and the sum of the first n terms S(n). (a)1458,486,162,54,. ..,2 a = 1458, r = 1/3 T(n) = (1458) (1/3)^(n-1) = 1458/3^(n-1) 1458/3^(n-1) = 2 3^(n-1) = 729 3^(n-1) = 3^6 n = 7 S(n) = (1458) (1 - 1/3^n) / (1 - 1/3) S(7) = (1458) (1 - 1/3^7) / (1 - 1/3) = 2186 --------------------------------------------------- 2.Find the sum of the 4th term to the 10th term of the geometric sequence 2,4,8,16,... . a = 2, r = 2 S(n) = (2)(2^n - 1) / (2-1) = (2)(2^n - 1) S(10) - S(3) = (2)(2^10 - 1) - (2)(2^3 - 1) = 2032 --------------------------------------------------- 3.The 1st term of a geometric sequence is 1/3 and the 4th term is -1/81. (a)Find the common ratio of the geometric sequence. T(n) = (1/3) r^(n-1) T(4) = (1/3) r^3 = -1/81 r = -1/3 (b)Hence find the sum of the first 6 terms. S(n) = (1/3) [ 1 - (-1/3)^n ] / (1 + 1/3) S(6) = (1/3) [ 1 - (-1/3)^6 ] / (1 + 1/3) = 182/729
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