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What is the sum of odd integers from 35 to 85, inclusive? A
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30 Jun 2020, 09:18
30 Jun 2020, 09:18
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What is the sum of odd integers from 35 to 85, inclusive?
A) 1,560
B) 1,500
C) 1,240
D) 1,120
E) 1,100
A) 1,560
B) 1,500
C) 1,240
D) 1,120
E) 1,100
Re: What is the sum of odd integers from 35 to 85, inclusive? A
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30 Jun 2020, 19:42
30 Jun 2020, 19:42
1
In this problem, we can identify that this odd integers can be included as part of an arithmetic sequence whose first term is 35, its last term 85 and the constant difference is 2. When it mentions the word inclusive, it means that the endpoints must be included in the sum.
To solve this problem, we can apply the formula of sum of "n" terms in an arithmetic progression:
(n*(Tn+t1))/2........................................................(1)
Where
t1=First term
Tn=Term "n"
n =Number of terms
But, to apply this formula, we need the number of terms "n".
To get this value, we modify the formula of arithmetic progression: tn=t1+r(n-1).
Changing it to to:
n=1+(tn-t1)/(r)................................................................(2)
Replacing values:
n=1+(85-35)/2
n=26
Using this value of n in equation (1)
Sum=(26*(85+35))/2
Result:
Sum=1560
To solve this problem, we can apply the formula of sum of "n" terms in an arithmetic progression:
(n*(Tn+t1))/2........................................................(1)
Where
t1=First term
Tn=Term "n"
n =Number of terms
But, to apply this formula, we need the number of terms "n".
To get this value, we modify the formula of arithmetic progression: tn=t1+r(n-1).
Changing it to to:
n=1+(tn-t1)/(r)................................................................(2)
Replacing values:
n=1+(85-35)/2
n=26
Using this value of n in equation (1)
Sum=(26*(85+35))/2
Result:
Sum=1560
Re: What is the sum of odd integers from 35 to 85, inclusive? A
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18 Sep 2020, 15:00
18 Sep 2020, 15:00
jpalaciosm wrote:
But, to apply this formula, we need the number of terms "n".
To get this value, we modify the formula of arithmetic progression: tn=t1+r(n-1).
Changing it to to:
n=1+(tn-t1)/(r)................................................................(2)
To get this value, we modify the formula of arithmetic progression: tn=t1+r(n-1).
Changing it to to:
n=1+(tn-t1)/(r)................................................................(2)
What does "r" mean in this formula?
