[問題]GWD4-25

[Chang,Stella]

In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?

A. 2^18
B. 3(2^17)
C. 7(2^16)
D. 3(2^16)
E. 7(2^15)

ANS:E

我選C, 想法是2的次方循環是2.4.8.6, 所以16th尾數8, 17th尾數6, 18th尾數2, 所以總合尾數選6的, 而E的尾數是8啊???
請教大家！謝謝！

[DARY]

In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?

A. 2^18
B. 3(2^17)
C. 7(2^16)
D. 3(2^16)
E. 7(2^15)

ANS:E

我選C, 想法是2的次方循環是2.4.8.6, 所以16th尾數8, 17th尾數6, 18th尾數2, 所以總合尾數選6的, 而E的尾數是8啊???
請教大家！謝謝！

16th=2^15
17th=2^16
18th=2^17

16th+17th+18th=2^15+2^16+2^17=(1+2+4)*(2^15)=7(2^15)

如果照你用尾數的話也沒有錯2^15尾數是4喔!!
你可能把2^15和15th搞錯了

[Chang,Stella]

In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?

A. 2^18
B. 3(2^17)
C. 7(2^16)
D. 3(2^16)
E. 7(2^15)

ANS:E

我選C, 想法是2的次方循環是2.4.8.6, 所以16th尾數8, 17th尾數6, 18th尾數2, 所以總合尾數選6的, 而E的尾數是8啊???
請教大家！謝謝！

16th=2^15
17th=2^16
18th=2^17

16th+17th+18th=2^15+2^16+2^17=(1+2+4)*(2^15)=7(2^15)

如果照你用尾數的話也沒有錯2^15尾數是4喔!!
你可能把2^15和15th搞錯了

不好意思, 我怎麼算2^15尾數都是8吔, 2^15+2^16+2^17=依序其尾數為8+6+2=16, 所以我會去找尾數也是6的C
謝謝你的回覆, 請Dary指正！

[liwuu]

In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?

A. 2^18
B. 3(2^17)
C. 7(2^16)
D. 3(2^16)
E. 7(2^15)

ANS:E

我選C, 想法是2的次方循環是2.4.8.6, 所以16th尾數8, 17th尾數6, 18th尾數2, 所以總合尾數選6的, 而E的尾數是8啊???
請教大家！謝謝！

16th=2^15
17th=2^16
18th=2^17

16th+17th+18th=2^15+2^16+2^17=(1+2+4)*(2^15)=7(2^15)

如果照你用尾數的話也沒有錯2^15尾數是4喔!!
你可能把2^15和15th搞錯了

不好意思, 我怎麼算2^15尾數都是8吔, 2^15+2^16+2^17=依序其尾數為8+6+2=16, 所以我會去找尾數也是6的C
謝謝你的回覆, 請Dary指正！

你的推算少了將答案前面的常數算進去,所以其實E的尾數,是6唷...不是8
同理,選項C的尾數不是6,而是2
E: 7(2^15)
2^15的尾數是8沒錯,但你將7乘進去,這樣子尾數是6!!

因此,算法建議以Dary大的方式來計算,最保險!!

[Chang,Stella]

In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th, and 18th terms in the sequence?

A. 2^18
B. 3(2^17)
C. 7(2^16)
D. 3(2^16)
E. 7(2^15)

ANS:E

我選C, 想法是2的次方循環是2.4.8.6, 所以16th尾數8, 17th尾數6, 18th尾數2, 所以總合尾數選6的, 而E的尾數是8啊???
請教大家！謝謝！

16th=2^15
17th=2^16
18th=2^17

16th+17th+18th=2^15+2^16+2^17=(1+2+4)*(2^15)=7(2^15)

如果照你用尾數的話也沒有錯2^15尾數是4喔!!
你可能把2^15和15th搞錯了

不好意思, 我怎麼算2^15尾數都是8吔, 2^15+2^16+2^17=依序其尾數為8+6+2=16, 所以我會去找尾數也是6的C
謝謝你的回覆, 請Dary指正！

你的推算少了將答案前面的常數算進去,所以其實E的尾數,是6唷...不是8
同理,選項C的尾數不是6,而是2
E: 7(2^15)
2^15的尾數是8沒錯,但你將7乘進去,這樣子尾數是6!!

因此,算法建議以Dary大的方式來計算,最保險!!

謝謝liwuu的解說, 也謝謝Dary的好思路, 每次有疑惑, 總有liwuu的幫忙, 真好！
p.s記得liwuu好像也幫我解過一題類似題, 唉, Stella真是笨啊