The defining characteristic of all geometric sequences is a common ratio which is a constant when dividing any term by the term preceding it.
In this case the common ratio is: -6/9=4/-6=r=-2/3
An infinite series will have a sum when r^2<1, so in this case the sum will converge to an actual value because (-2/3)^(+oo) approaches zero.
The sum of any geometric sequence is:
s(n)=a(1-r^n)/(1-r), since we have a common ratio of -2/3 and we want to calculate an infinite series, ie, n approaches infinity, the sum becomes simply:
s(n)=a/(1-r) (because (1-r^+oo) approaches 1 as n approaches +oo)
So our infinite sum is:
s(+oo)=9/(1--2/3)
s(+oo)=9/(1+2/3)
s(+oo)=9/(5/3)
s(+oo)=27/5
s(+oo)=54/10
s(+oo)=5.4
Answer:Total units would be: 3+4 = 7. value of 1 unit = 28/7 = 4. ratio would be 3(4) & 4(4) = 12 & 16
Step-by-step explanation:
Answer:
$6.22
Step-by-step explanation:
Given;
Total number of coins N = 50
Number of pennies p = 14% of N = 0.14 × 50 = 7
Number of dimes d = 32% of N = 0.32×50 = 16
Number of nickels n = 4 + number of pennies = 4+p
n = 4+7 = 11
Number of quarters q;
N = p+d+n+q
q = N - (p+d+n)
q = 50-(7+16+11)
q = 16
1 Penny = 1 cent = $0.01
1 Nickel = 5 cent = $0.05
1 dime = 10 cents = $0.10
1 quarter = 25 cents = $0.25
Total amount in the bag is;
C = 0.01p + 0.05n + 0.10d +0.25q
Substituting the values;
C = 0.01(7) + 0.05(11) + 0.10(16) + 0.25(16)
C = $6.22
The bag contains $6.22
Answer:280-10/5 (everything over/divided by 5)
Step-by-step explanation:
280 is all the students 10 go in car so subtract that and divide the answer by 5.
Answer:
x=7
Step-by-step explanation:
2x=20-6
2x=14
x=14/2
x=7
