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F5 Maths sequence

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43.. Find the sum to infinity of the geometric sequence x, -1, 1 / x, -1/ x^2, ...,where x > 1.47. The measures of the interior angles of an n-sided polygon are in arithmetic sequence. If the largest angle is 160 degree and the common difference is 5 degree, find n.48. Three numbers are in arithmetic... 顯示更多 43.. Find the sum to infinity of the geometric sequence x, -1, 1 / x, -1/ x^2, ..., where x > 1. 47. The measures of the interior angles of an n-sided polygon are in arithmetic sequence. If the largest angle is 160 degree and the common difference is 5 degree, find n. 48. Three numbers are in arithmetic sequence. If their sum is 15 and their product is 105, then the largest number is 50. In an arithmetic sequence, the sum of the first 20 terms is 370 and the sum of the next 20 terms is 1570. What is the first term?

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43. T(1) = a = x common ratio R = -1/x sum to infinity of the geometric sequence = a/(1-R) => x/(1+1/x) = x^2/(1+x) 47. T(1) = a T(n) = a + 5*(n-1) = 160 sum of arithmetic sequence = n/2 [T(1) + T(n)] = 180*(n-2) (sum of interior angle of polygon) => n/2 [a + 160] = 180n - 360 n = 9 or -16 (neg.) 48. sum of arithmetic sequence = 3/2 [T(1) + T(3)] = 15 T(1) + T(3) = 10 a+d = 5 => T(2) = 5 T(1) * T(2) * T(3) = 105 => T(1) * T(3) = 21 the largest number is 7. 50. S(20) = 20/2 [2a+19d] = 370 => [2a+19d] = 37 S(40) = 40/2 [2a+39d] => [2a+39d] = (370+1570)/20 = 97 d = 3, a = -10

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