PP-T1-DS-217

[lucyyeh]

a1 , a2 , a3 , . . . , a15

In the sequence shown, an = an - 1 + k, where 2<=n<=15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10 ?

(1) a1 = 24

(2) a8 = 10

ANS:B
全無頭緒怎麼解的

[scottkidd]

a1 , a2 , a3 , . . . , a15

In the sequence shown, an = an - 1 + k, where 2<=n<=15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10 ?

(1) a1 = 24

(2) a8 = 10

ANS:B
全無頭緒怎麼解的

題目說要"greater than 10 "，an又是 = an - 1 + k，k is a nonzero constant。
所以a8=10=a7+k → a7一定<10，a9=a8+k=10+k一定就大於10囉

[a-jan]

請問樓主..
(1) 條件不充份的原因，是因為 a1=24 代入 an = an - 1 + k 之下... ==> a1-1= a0 ..因題目只提到 a1.......a15，因此超出題目要求的範圍嗎?

謝..

[chris8888]

In the sequence shown, an = an - 1 + k, where 2<=n<=15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10 ?

(1) a1 = 24
a2 = a1 + k => a2 = 24 + k
a3 = a2 + k => a3 = 24 + 2k
a4 = a3 + k => a4 = 24 + 3k
不知到k到底是positive or negative 也不知到 k的大小, 通通會影響>10的個數 insufficient
比方說若k=-15, 那麼全都<10
(2) a8 = 10
a7 = a6 + k => a6 = 10 - 2k
a8 = a7 + k => a7 = 10 - k
a9 = a8 + k => a9 = 10 + k
a10 = a9 + k => a10 = 10 + 2k
a11 = a10 + k => a11 = 10 + 3k
由於已知的數據是10, k不管大小, 都會影響10變成大於10或小於10, 可以推論
由此可見假若k>0, 那麼從a9 ~ a15有七個大於10 ; 反之, 假若k<0, a8 ~ a2有七個大於10

[william0625]

In the sequence shown, an = an - 1 + k, where 2<=n<=15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10 ?



(1) a1 = 24

a2 = a1 + k => a2 = 24 + k

a3 = a2 + k => a3 = 24 + 2k

a4 = a3 + k => a4 = 24 + 3k

不知到k到底是positive or negative 也不知到 k的大小, 通通會影響>10的個數 insufficient

比方說若k=-15, 那麼全都<10

(2) a8 = 10

a7 = a6 + k => a6 = 10 - 2k

a8 = a7 + k => a7 = 10 - k

a9 = a8 + k => a9 = 10 + k

a10 = a9 + k => a10 = 10 + 2k

a11 = a10 + k => a11 = 10 + 3k

由於已知的數據是10, k不管大小, 都會影響10變成大於10或小於10, 可以推論

由此可見假若k>0, 那麼從a9 ~ a15有七個大於10 ; 反之, 假若k<0, a8 ~ a2有七個大於10

k>0, 那麼從a9 ~ a15有七個大於10 ; 反之, 假若k<0, a8 ~ a2有七個大於10
k>0k<0這樣不就有兩種解
還是只算一種解　可以解釋一下嗎
抱歉腦筋轉不太過來

[Philosophia]

In fact point of (B) is that A8 is in the middle of 15. As a result, when A8 is in the middle of 15 sequence and A8 = 10, it is not important k > 0 or k <0 - there are 7 terms in the sequence are greater than 10.

[william0625]

In fact point of (B) is that A8 is in the middle of 15. As a result, when A8 is in the middle of 15 sequence and A8 = 10, it is not important k > 0 or k <0 - there are 7 terms in the sequence are greater than 10.

阿
想歪了
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