The general term of an infinite geometric sequence is given by:
T(n)= 6[(x+1)/8]^n
(a) Find the range of the values of x for which the sum to infinity exists
(b) Find the sum to infinity of the sequence in terms of x.
(c) If the sum to infinity of the sequence is 18, find the value of x.
點解AND 點做?
MATH F6
2012-09-17 2:14 am
回答 (1)
2012-09-17 4:41 pm
✔ 最佳答案
Let a, r be the first term and the common ratio of the GS T(n), therefore,a = T(1) = 6(x + 1)/8 = 3(x + 1)/4
r = T(2)/T(1) = (x + 1)/8
(a) If the sum to infinity exist, then |r| < 1, ie.
-1 < (x + 1)/8 < 1
-8 < (x + 1) < 8
-9 < x < 7 ... (Ans)
(b) Sum to infinity
= a/(1 - r)
= [3(x + 1)/4]/[1 - (x + 1)/8]
= 6(x + 1)/(7 - x) ... (Ans)
(c) If the sum is 18, then
6(x + 1)/(7 - x) = 18
x + 1 = 3(7 - x)
x + 1 = 21 - 3x
x = 5 ... (Ans)
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