#1

Alright, these are messing me up, so...

4. The sum to infinity of a geometric series if four times its first term. Find the common ratio.

3. How many terms of the arithmetic series 15+13+11... are required to make a total of -36?

4. The sum to infinity of a geometric series if four times its first term. Find the common ratio.

3. How many terms of the arithmetic series 15+13+11... are required to make a total of -36?

#2

3) a = 15 d = -2

Sn = n/2 (a + (n - 1) d)

-36 = n/2 (15 + (n - 1) -2)

-72 = n (15 - 2n + 2)

2n^2 - 17n + 72 = 0

(2n - 9)(n - 8) = 0

n = 8 or n = 9/2

Sn = n/2 (a + (n - 1) d)

-36 = n/2 (15 + (n - 1) -2)

-72 = n (15 - 2n + 2)

2n^2 - 17n + 72 = 0

(2n - 9)(n - 8) = 0

n = 8 or n = 9/2

#3

Dammit! I didn't times out the 2, that's where I went wrong. Cheers!

#4

Alright, these are messing me up, so...

4. The sum to infinity of a geometric series if four times its first term. Find the common ratio.

3. How many terms of the arithmetic series 15+13+11... are required to make a total of -36?

4.

S-inf = a/1-r

a/1-r=4a

a = 4a-4ar

1=4-4r

r=3

Edit:

Damn;

4r=3

r=3/4

*Last edited by bequickorbedead at May 30, 2008,*

#5

4.

S = u/(1-r)

in this case becomes

4u = u/(1-r)

4u(1-r) = u

=> 1-r = 1/4

r = 3/4

Dude, condition for Sum to infinity to hold is that r < 1.

EDIT again, sorry, seems you realised yourself (-:

S = u/(1-r)

in this case becomes

4u = u/(1-r)

4u(1-r) = u

=> 1-r = 1/4

r = 3/4

4.

S-inf = a/1-r

a/1-r=4a

a = 4a-4ar

1=4-4r

r=3

Dude, condition for Sum to infinity to hold is that r < 1.

EDIT again, sorry, seems you realised yourself (-:

*Last edited by Mad_BOB at May 30, 2008,*

#6

Ahh, brilliant

I've just finished two chapters

I've just finished two chapters

#7

haha brain hurts from reading the questions

i took the exam 2 weeks ago pheeew

EDIT: core 2?

i took the exam 2 weeks ago pheeew

EDIT: core 2?

#8

3) a = 15 d = -2

Sn = n/2 (a + (n - 1) d)

-36 = n/2 (15 + (n - 1) -2)

-72 = n (15 - 2n + 2)

2n^2 - 17n + 72 = 0

(2n - 9)(n - 8) = 0

n = 8 or n = 9/2

i would like to correct this one

3) a = 15 d = -2

Sn = n/2 (

**2**a + (n - 1) d)

-36 = n/2 (30 + (n - 1) -2)

-72 = n (30 - 2n + 2)

-72 = 32n -2n^2

2n^2 - 32n

**-**72 = 0

(2n + 4)(n - 18) = 0

n = 18 or (n = -2 which it cannot be)

#9

Ah crap.

I knew it was off with it giving 2 answers

I knew it was off with it giving 2 answers