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.

_________________

At the still point, there the dance is. -- T.S. Eliot

Formerly genxer123