Find the sum of the sequence.
38+39+40+41+...+137
The sum is?
My answer 175(99)= 17,325
Is this correct? If not how do I get the correct answer?
no, no.
first: there are 100 terms here.
second, how did you get 175 as the mean? 175 is greater than the highest term? The mean is 175/2
the mean is 137+38 divided by 2
one hundred terms x mean=below
sum= 100(38+137)/2=175*50=8750
To find the sum of an arithmetic sequence, you can use the formula:
Sum = (n/2)(first term + last term)
In this case, the first term is 38 and the last term is 137. So, applying the formula:
Sum = (n/2)(38 + 137)
To find the number of terms (n), we can use the formula for the nth term of an arithmetic sequence:
nth term = first term + (n-1)(common difference)
Here, the common difference is 1. Let's solve for n:
137 = 38 + (n-1)(1)
137 - 38 = n - 1
99 = n - 1
n = 100
Now we can substitute n = 100 back into the sum formula:
Sum = (100/2)(38 + 137)
Sum = 50(38 + 137)
Sum = 50(175)
Sum = 8,750
Therefore, the correct sum of the sequence 38+39+40+41+...+137 is 8,750, and not 17,325 as you mentioned.
To find the sum of a sequence, we can use the formula for the sum of an arithmetic series:
Sum = (n/2) * (first term + last term)
In this case, the first term is 38 and the last term is 137. We can find the number of terms, n, by subtracting the first term from the last term and adding 1:
n = last term - first term + 1
n = 137 - 38 + 1
n = 100
Now, we can substitute the values into the sum formula:
Sum = (100/2) * (38 + 137)
Sum = 50 * 175
Sum = 8,750
So, the correct answer is 8,750, not 17,325.