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
版主: shpassion, Traver0818
lucyyeh \$m[1]: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
chris8888 \$m[1]: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
Philosophia \$m[1]: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.
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