Series and Sequence help. (1 Viewer)

[williamc]

1) The first term of an arithmetic series is 4 and the fifth term is four times the third term. Find the common difference. (got nfi)


2) Loan of $1000 is to be repaid by equal annual instalments, repayments commencing at the end of the first year of the loan, at the rate of 10% is calculated each year, and added to the balance.

If the annual installment is P dollars. find
i) the amount owing at the beginning of the second year of the loan.
ii)The amount owing at the beginning of the third year of the loan.
iii)Prove that if the loan(including interest charges) is repaid at the end of n years then

P=1000/1-1/1.1^n

Working

P=1000 r=10/100

A1=1000(1+10/100)^1-M
=1000(1.1)-m

i) A2=Ai(1.1)-M
=(1000(1.1)-M)(1.1-M)
=1000(1.1)^2-M(1.1)-M
=1000(1.1)^2-M(1+1.1)
How do you get the actual amount.

ii) A3=A2(1.1)-M
=(1000(1.1)^2-M(1+1.1))(1.1)-M
=1000(1.1)^3-M(1+1.1+1.1^2)
Geometric
a=1 r=1.1 n=?
But n is unknown so can't use the Sn= a(r^n-1)/r-1 .. How to get the actual amount?

CRAP i just realised M is for monthly repayments?
iii) got no idea

 

[watatank]

1) The first term of an arithmetic series is 4 and the fifth term is four times the third term. Find the common difference. (got nfi)

T₁ = a = 4

T₅ = 4 + 4d

but T₅ = 4*T₃

= 4(4 + 2d)

therefore

4 + 4d = 4(4 + 2d)

4 + 4d = 16 + 8d

4d = -12

d = -3

if you want to check..if d is correct then the series is 4, 1, -2, -5, -8.

that seems to work perfectly fine with all the information given, so yeah.