The common difference of an arithmetic sequence is d, where d is not equal to 0. The 9th term of the sequence is three times the 5th term.
a)Express the general term T(n) of the sequence in trm of d and n
b)The 11th term is twice the kth term. Find the value of k.
c)Find T(8):T(4).
等差數列求解,唔識express the general term T(n)?
2016-05-17 10:25 am
回答 (2)
2016-05-17 10:36 am
✔ 最佳答案
Let a be the first term, then T(n) = a + (n - 1)dT(9) = 3 × T(5)
a + 8d = 3 × (a + 4d)
a + 8d = 3a + 12d
2a = -4d
a = -2d
(a)
Therefore, T(n) = -2d + (n - 1)d = (n - 3)d
(b)
T(11) = 2 × T(k)
8d = 2 × (k - 3)d
k - 3 = 4
k = 7
(c)
T(8) : T(4)
= 5d : d
= 5 : 1
2016-05-19 3:27 pm
thank you so much
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