math doubts [NEW]

[simba]

each year a company gives a grant to charity. The amount given each year increases by 5% of its value in the preceding year. The grant in 2001 was $5000. Find :

(i) the grant given in 2011
(ii) the total amount of money given to the charity during the years 2001 to 2011 inclusive

[astarmathsandphysics]

I will answer when i get home in 3 hours

[astarmathsandphysics]

each year a company gives a grant to charity. The amount given each year increases by 5% of its value in the preceding year. The grant in 2001 was $5000. Find :

(i) the grant given in 2011
(ii) the total amount of money given to the charity during the years 2001 to 2011 inclusive
i)
ii)

[simba]

hw did u change da 5% to 1.05

[Eamyzz]

r=1+5/100 is hw they gt 1.05
anythng else? =)

[simba]

the second term of a geometric progression is 3 and the sum to infinity is 12
(i) find the first term of the progression



will someone solve it

[simba]

q11 june 06 in part (i)  urgently plz

[slvri]

the second term of a geometric progression is 3 and the sum to infinity is 12
(i) find the first term of the progression



will someone solve it

the nth term of a GP is given by a_n=ar^n-1
for the second term n=2
ar^2-1=3
ar=3
a=3/r
the sum to infinity of a GP is given by S=a/(1-r)
a/(1-r)=12
a=12(1-r)
put a=3/r
3/r=12(1-r)
3=12r(1-r)
3=12r-12r²
12r²-12r+3=0
4r²-4r+1=0
(2r)²-2(2r)(1)+(1)²=0
(2r-1)²=0
2r-1=0
r=1/2
a=3/(1/2)=6
is this the correct answer?

[Eamyzz]

yes i gt da same answer tooo 

[simba]

guyz another question ....num.4 in nov.07

will someone help :

[Ghost Of Highbury]

guyz another question ....num.4 in nov.07

will someone help :

A level maths --> paper no?

[simba]

its paper 1 ...pure 1

[badboy]

each year a company gives a grant to charity. The amount given each year increases by 5% of its value in the preceding year. The grant in 2001 was $5000. Find :

(i) the grant given in 2011
(ii) the total amount of money given to the charity during the years 2001 to 2011 inclusive
i)
ii)

ur answers r wrong i) 8144 ii)71034

[slvri]

ur answers r wrong i) 8144 ii)71034

(i)the grant given in 2011 should be the 11th term
the 11th term is given by a₁₁=ar^n-1=5000*1.05^11-1=5000*1.05¹⁰=$8144
(ii)total amount is the sum of the money from 2001 to 2011
so the sum from terms 1 to 11 is S₁₁
=a(1-rⁿ)/1-r
=5000(1-1.05¹¹⁾)/1-1.05
=5000(1-1.05¹¹)/-0.05
=$71034
hope this helped

[astarmathsandphysics]

Sod it you are righht. I shouldn't do these questions first thing in the morning.