Geometric Sequence Urgent!

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2010-02-18 2:46 am

QS1: In a G.P it is given that a = -6/16 Tn=-16/9 Sn=-781/144 find n and R

QS2: In a G.P, the first term is a, the nth term is b and the sum of the first n terms is S. Find the common ratio

更新1:

a = -9/16 not -6/16

回答 (1)

用戶2053

2010-02-18 6:22 am

✔ 最佳答案

Why -6/16 not written as -3/8 ?

2010-02-17 22:22:40 補充：
Q1)
Tn = aR^(n-1) = -16/9
(-9/16)R^(n-1) = -16/9
R^(n-1) = 256/81.....(*)
R^n = 256R/81
;;;;;;;;;;;;;;;;;;;;;;;;;
Sn = a(1 - R^n) / (1 - R) = -781/144
(-9/16)(1 - 256R/81) / (1 - R) = -781/144
(1 - 256R/81) / (1 - R) = 12496/1296 = 781/81
81(1 - 256R/81) = 781(1 - R)
81 - 256R = 781 - 781R
525R = 700
R = 4/3 , sub it to (*) :
(4/3)^(n-1) = 256/81 = 4^4 / 3^4
n - 1 = 4
n = 5
Q2
nth term = b = ar^(n-1)
r^(n-1) = b/a
r^n = br/a
sum of the first n terms = a(1 - r^n) / (1 - r) = S
a(1 - br/a) / (1 - r) = S
a - br = S(1 - r)
a - br = S - Sr
(S - b)r = S - a
r = (S - a) / (S - b)

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