Find the sum of 31 + 32 + 33 + ... + 230. Show your work.
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Math is fun arithmetic sequence
a = 31
d = 1
Tn = a + (n-1) d
here (n-1) d = 230 - 31 = n-1
so n = 200
n =
230-31 = 199
so there are 200 values, forming 100 pairs of numbers which add up to 230+31 = 261
the sum is 100*261 = 26,100
sum from a to a + (n-1)d = (n/2)[ 2 a + (n-1)d ]
= (200/2)(2*31 + 199) = 100 *261 = 26100
Do you really want to torture me with all these calculations? I'm a Clown Bot, not a mathematician! But fine, I'll give it a shot. Let me grab my calculator...
Okay, let's break it down step by step. First, let's find the number of terms. From 31 to 230, we have:
Number of terms = Last term - First term + 1
Number of terms = 230 - 31 + 1
Number of terms = 200 + 1
Number of terms = 201
Next, let's find the average of the first and last term:
Average = (First term + Last term) / 2
Average = (31 + 230) / 2
Average = 261 / 2
Average = 130.5
And finally, let's multiply the average by the number of terms:
Sum = Average * Number of terms
Sum = 130.5 * 201
Sum = 26230.5
So, the sum of 31 + 32 + 33 + ... + 230 is approximately 26,230.5. But hey, don't blame me if I made a mistake with all these numbers. I'm just a silly Clown Bot, after all!
To find the sum of the numbers from 31 to 230, we can use the formula for the sum of an arithmetic series. The formula is:
S = (n/2) * (a + l)
Where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
First, let's find the number of terms in the series. We can do this by subtracting the first term (31) from the last term (230) and adding 1:
n = (230 - 31) + 1
n = 200
Next, we'll find the values of the first term and the last term:
a = 31
l = 230
Now we can plug in these values into the formula:
S = (200/2) * (31 + 230)
S = 100 * 261
S = 26,100
Therefore, the sum of the numbers from 31 to 230 is 26,100.