我想問下呢題數點計??

用戶20139

2008-06-09 2:50 am

設數列An的通項An=3n+2,n=1,2,3.....則An前19項的和為
A,551 B,570
C,608 D,670
最主要解釋,唔該...唔好有d白痴仔亂撞答案唔該==

更新1:

我都知呢個方法,但話..An前19項既和ma,唔係應該 3(n-19)+2+3(n-18)+2+3(n-17)+2+..............+3n+2咩? 我gag到佢既意思就係咁... 假如你既計法,係指..An頭19項的和~~有冇錯?

更新2:

查實,我都知你個個方法..但係同條題目意味不合....哈,其實我係中六學生...你個方法我小六已經識........我想問既唔係你想講既野.....我知你係中三學生=="因為你問個d數,我都完全知係咩黎......亦都識計同識解......

回答 (2)

碧咸仔

2008-06-09 3:20 am

✔ 最佳答案

3n+2 = Tn

you need to use the numeral theory to find the S(n)
but i think you are not a form 6 student
use the tranditional method

sum of first 19 term
3(1)+2 + 3(2) + 2 + 3(3) +2 +..... + 3(19) +2

there are 19 * 2 = 38
we cover the 19 (2)
there are
3+3*2+3*3+..........3*19
factorization
3 ( 1+ 2+3+....+19)
using (頭+尾) 乘項數除2
19(1+19 )*0.5 = 190
3*190=570
sum of first 19 term 570+38 = 608

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fionagung

2008-06-13 7:54 am

the sequence of An=3n+2,n=1,2,3..... will be 5,8,11.......
S19 = n/2 [ 2a + (n-1) d ]
= 19/2 [ 10 + (18)(3) ]
= 608

參考: F.5 knowledge

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