Geometric Progression G.P.

[匿名]

2008-07-15 2:42 am

1. The 3rd and 7th term of a geometric progression are 1/4 and 4 respectively. Find
(a) the common ration R
(b) the first term a

2. $1000 is deposited in a bank on the first day of each month for 4 years and the interest rate is 8% per annum. Find the total amount accumulated at the end of the fourth year. (Correct to the nearest dollar)

3. A mobile priced at $5,988 can be bought and paid by instalments at 2% per month for 6 months. Find how much has to be paid each month.

Questions 2 and 3 with 中文解題.. .. thank you very much!

回答 (1)

STEVIE-G™

2008-07-15 3:33 am

✔ 最佳答案

1
Let the general term T(n)=aR^n , where a is the first term and R be the common ratio
The 3rd and 7th term of a geometric progression are 1/4 and 4 respectively
aR^3=1/4-----------1
aR^7=4-----------2
2/1:
R^4=16
R=2
Sub R=2 into 1
a=1/32
2.
the total amount accumulated at the end of the fourth year
=第一年所累積的金錢+第二年所累積的金錢+第三年所累積的金錢+第四年所累積的金錢
=1000(1+8%)^4+1000(1+8%)^3+1000(1+8%)^2+1000(1+8%)
=1000[(1+8%)^4+(1+8%)^3+(1+8%)^2+(1+8%)]
=1000[1.08(1.08^4-1)/(1.08-1)]
=$4867
3.
Let the money paid each month be $x
第一個月所付金錢+第二個月所付金錢+第三個月所付金錢+第四個月所付金錢+第五個月所付金錢+第六個月所付金錢
x(1+2%)^6+x(1+2%)^5+x(1+2%)^4+x(1+2%)^3++x(1+2%)^2++x(1+2%)=5,988
x[1.02(1.02^6-1)/(1.02-1)]=5988
x=931

👍 0 👎 0