Answer:
(c) an = 4·(1/3)^(n-1)
Step-by-step explanation:
The explicit rule for a geometric sequence with first term a1 and common ratio r is ...
an = a1·r^(n-1)
The factor in the recursive rule tells you the common ratio is 1/3, so the explicit rule is ...
an = 4·(1/3)^(n-1) . . . . . . matches choice C
Answer:
He invested $8500 with rate 3 1/5%
He invested $3000 with rate 3%
Step-by-step explanation:
* <em>Lets revise the rule of the simple interest</em>
- Simple interest I = PRT, where P in the money invested, R is the
interest rate and T is the time of investment
- Phyllis invested $11,500
- A portion earning a simple interest rate of 3 1/5% (3.2%) per year
- The rest earning a rate of 3% per year
- After one year the total interest earned on these investments
was $362.00
- We need to find the amount of money invested in each rate
* Assume that he invested $x with rate 3 1/5% and $y with rate 3%
∵ He invested $11,500 in both rates
∴ x + y = 11,500 ⇒ (1)
∵ He invested $x with 3 1/5%
∵ P = $x
∵ R = 3.2/100 = 0.032
∵ T = 1
∴
∴
∵ He invested $y with 3%
∵ P = $y
∵ R = 3/100 = 0.03
∵ T = 1
∴
∴
∵ The total interest was $362.00
- The total interest = +
∴ 0.032x + 0.03y = 362.00 ⇒ (2)
<em>We have system of equations</em>
x + y = 11,500 ⇒ (1)
0.032x + 0.03y = 362.00 ⇒ (2)
Multiply equation (1) by -0.03 to eliminate y
-0.03x - 0.03y = 345 ⇒ (3)
Add equations (2) and (3)
0.002x = 17
Divide both sides by 0.002
x = 8500
Substitute the value of x in equation (1)
8500 + y = 11,500
Subtract 8500 from both sides
y = 3000
* He invested $8500 with rate 3 1/5%
* He invested $3000 with rate 3%
