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
Jay's claim is false. They would have $156.8 left which is 56% of their original combined total.
Answer:
$3283.2
Step-by-step explanation:
Given data
Principal= $2700
Rate= 4%
Time= 5 years
Required
the final Amount A
The compound interest formula is
A=P(1+r)^t
Substitute
A=2700(1+0.04)^5
A=2700(1.04)^5
A=2700*1.216
A=$3283.2
Hence the balance in the account after 5 years is $3283.2
Answer:
Step-by-step explanation:
angle 4 is congruent to angle 4 because they are alternate interior angles.
angle 5 is congruent to angle 3 because they are alternate interior angles.
angle 1+angle 2+angle 3 is equal to (=) angle 1+angle 2+angle 3
angle 1+angle 2+angle 3=180 degree(being sum of interior angles of a trianngle)
