What symbol makes the statement true? 4/6 3/8
2 answers:
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Answer:
sum is 125,500
sum in summation notation is = (2a+(n-1)d)n/2
Step-by-step explanation:
This problem can be solved using concept of arithmetic progression.
The sum of n term terms in arithmetic progression is given by
sum = (2a+(n-1)d)n/2
where
a is the first term
d is the common difference of arithmetic progression
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in the problem
series is multiple of 4 starting from 4 ending at 1000
so series will look like
series: 0,4,8,12,16..................1000
a is first term so
here a is 0
lets find d the common difference
common difference is given by nth term - (n-1)th term
lets take nth term as 8
so (n-1)th term = 4
Thus,
d = 8-4 = 4
d can also be seen 4 intuitively as series is multiple of four.
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let calculate value of n
we have last term as 1000
Nth term can be described
Nth term = 0+(n-1)d
1000 = (n-1)4
=> 1000 = 4n -4
=> 1000 + 4= 4n
=> n = 1004/4 = 251
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now we have
n = 1000
a = 0
d = 4
so we can calculate sum of the series by using formula given above
sum = (2a+(n-1)d)n/2
= (2*0 + (251-1)4)251/2
= (250*4)251/2
= 1000*251/2 = 500*251 = 125,500
Thus, sum is 125,500
sum in summation notation is = (2a+(n-1)d)n/2
Answer:
amount is 1000 ×
$40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years
rate 14.97 % when Donna's account will have a balance of 1 million dollars in 40 years when principal is $2500
Step-by-step explanation:
principal = $1000
rate = 8 % = 0.08
to find out
the future value, S(t)
principal when Donna's account will be 1 million dollars when she retires in 40 year
at what rate Donna's account will have a balance of 1 million dollars in 40 years
solution
we know compounded continuously formula i.e.
amount = principal × ..................1
put the value principal and rate in equation 1 to find amount any time
amount = principal ×
amount = 1000 ×
in 2nd part we have time 40 year and amount 1 million so put rate amount and time in equation 1 to find principal
rt = 0.08 × 40 = 3.2
amount = principal ×
1000000 = principal ×
principal = 1000000 /
principal = 1000000 / 24.5325302
principal = 40762.20397
so $40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years
in 3rd part we have amount 1 million and principal $2500 and time 40 year put all these in equation 1 to find rate
amount = principal ×
1000000 = 2500 ×
take ln both side
ln = ln (1000000 / 2500 )
40 r = ln 400
r = ln (400) / 40
r = 0.149787
so rate 14.97 % when Donna's account will have a balance of 1 million dollars in 40 years when principal is $2500