ladyrenee95 wrote:
Are these formulas correct? I am having trouble with odd numbers for some reason.
N for odd numbers = (Last odd - First odd)/2)) +1
Sum of odd numbers = (First odd + Last odd)*N))/2
1. N = (59-41)/2))+1 = 10
2. Sum of odds = (41+59)*10))/2 = 500
3. 500 - 10 = 490 B
Also, on part 1 of my calculations, do you add one because it is inclusive and do not add one if it is not inclusive?
ladyrenee95 , sorry, I posted before I saw your questions.
Yes, your method is correct.
I think the reason you might be having trouble with odd numbers is that for consecutive odd integers, the interval (between the numbers), is two. Two is even; that could confuse. Or you might be forgetting to start with the first ODD term (e.g. here, first term is 41, not 40).
Bottom line: The "interval" between 1 and 3 is two. The interval between 2 and 4 is two. For consecutive odds and evens, in the formula, you divide by 2.
Take smaller numbers. Say, sum of odd integers from 0 to 6. So 1 + 3 + 5 = 9. There are three terms (1, 5, 9) whose sum is 9.
Number of terms in "odd integers from 0 to 6":
\(\frac{(Last - First)}{2}+ 1\)\(\frac{(5-1)}{2} + 1 = (\frac{4}{2}+ 1) = (2 + 1) = 3\) Correct
SUM:
(Average)(# of terms)\(\frac{(First + Last)}{2}(3)\)\(\frac{(1 + 5)}{2} (3) = (3)(3) = 9\)Bingo. Dividing by 2 for consecutive odd integers works.
When subtracting, you add one because subtraction doesn't include the first number. If in doubt: use small numbers that replicate your situation.
For example, # of terms from 1 to 4? The numerals are 1, 2, 3, 4. There are 4 terms. BUT (4 - 1) = 3.
We need one more. 3 + 1 = 4.
There's a mnemonic: "add one before you're done." It almost always applies. If in doubt, replicate your situation with small numbers. Rare in sequence sums but possible: If you see the word "exclusive" or the phrase "exclusive of," that is when you really need to check.
I have seen your other answers using this method. The ones I've seen are correct! (The one about -190 to 195? Correct, but long. -190 to +190 = 0; you are left with only 5 numbers to sum. STILL - correct.)
Here is a fantastically written, comprehensive post on
all kinds of sequences by
benjiboo ,
scroll down for arithmetic sequence And here is a thread on sequences.
VeritasPrepKarishma 's
posts are greatHope this barrage of information helps.
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