sequences/series - help needed (1 Viewer)

[Petinga]

1. The sum of the first 4 terms of an arithmetic sequence is 34 and the sum of the next 4 terms is 146. Find the sum of the 9th and 10th terms.

2. The rungs of a ladder decrease uniformly in length from 40cm at the bottom runf to 30cm at the top of rung. How many rungs are there if their total lenth is 5.25m?

3. The track of a gramophone record is the shape of a spiral curve and may be considered as a number of concentric circles of inner and outer radius 5.25cm and 10.5cm respectively. The record rotatates at 33 and 1/3 revs/min and tqakes 18 minutes to play. Find the length of the track.

4. For the series function defined by Sn= 3n^2 - 11n, find tn and hence show that the seqeunce is arithmentic.

 

[MarsBarz]

1. The sum of the first 4 terms of an arithmetic sequence is 34 and the sum of the next 4 terms is 146. Find the sum of the 9th and 10th terms.

1.

S4 = 34
S8-S4 = 146
S8-34 = 146
S8 = 180

S4 = 4/2[2a+(4-1)d]
     = 2(2a+3d)
     =4a+6d
.:. 34 = 4a+6d                    (1)
S8 = 8/2[2a+(8-1)d]
     = 4(2a+7d)
     = 8a+28d
.:. 180 = 8a+28d                (2)

Solving simultaneously

from (1),
4a = 34-6d
a = (34-6d)/4                     (3)
Sub (3) in (2),
8[(34-6d)/4]+28d = 180
68-12d+28d = 180
16d = 112
d = 7                                  (4)
Sub (4) in (3)
a = [34-6(7)]/4
   = -2

Alright, now that we've got values for a and b, find term 9 and term 10 (I assume that you didn't mean find sum of first 9 terms and sum of first 10 terms. If you did I'm sure you know what to do from here.) Anyway:

T9 = -2 + (9-1)7
     = 54
T10 = 54+7
       = 61

GGNORE

 

[MarsBarz]

2. The rungs of a ladder decrease uniformly in length from 40cm at the bottom runf to 30cm at the top of rung. How many rungs are there if their total lenth is 5.25m?

Info:
5.25m = 525cm
Arithmetic serie (uniform difference)

Let n be the number of rungs
Sn = n/2(a+l)
525 = n/2(30 + 40)
525 = n/2(70)
525 = 35n
n = 15
.:. There are 15 rungs.

GGNORE !

 

[FinalFantasy]

hihi!
what is "GGNORE!"?????????????????????????

 

[LostAuzzie]

4. For the series function defined by Sn= 3n^2 - 11n, find tn and hence show that the seqeunce is arithmentic.

Sn= 3n^2 - 11n
    = n(3n - 11)
    = n/2 (6n - 22)
Since Sn=n/2 (2a + d(n-1)) For an Arithmetic Series
2a - d = - 22
2a = d - 22
d = 6
2a = 6 - 22
     = - 16
a = - 8
Therefore: Tn = a + (n-1)d
                      = 6(n-1) - 8
                      = 6n - 14

I think that's how to answer it

EDIT: Made error in my calculations, fixed it up

 

[society's evil]

Gosh, I'm glad that I do not do mathematics anymoree!!!