## Math help?

Today in math we were asked this question

What is the sum of the first 300 odd numbers?

He said that there is an easier way to find the answer besides having to add it one by one on the calculator. Does anyone know how to get the answer?

I’m not here so you guys can do my homework, I seriously don’t know how I could do this.

Daaaang Mcfake, That sounded like another language. haha thxs

ITS SOMETHING LIKE:
299 (LAST ONE) + 1 (FIRST ONE) x 150 (THE # OF ODD #’S) / 2 (TAKES 2 TO MAKE A PAIR)
SO I THINK IT’S 300 x 150 / 2
=22,500?
OOPS THOUGHT IT SAID FIRST ODD NUMBERS UP TO 300
(599+1)(300)/2
=90,000

I have some questions that i need answered, and if I dont have them done by tomorrow i fail math. so please help.. thanks

1. TRUE OR FALSE : A negative number raised to an odd power will always be negative. is that true or false??

these are matching it says…Without using your calculator, choose an estimate from the column at the right for each of the following. here they are

1. 8 negative suared
2. 8 squared
3. 124 x 1/2
4. 11 to the 2.2 power
Here are the answers that go with these questions. they gave me more answers than questions.

A. 3 squared
B. 1/3
C. 3
D. 11 suared
E. 11
F. 1/9

1)True

1. = 1/64……….F?
2. = 64……….D?
3. = 62…………D?
4. = 195………..D?

The choices really dont match the questions at all.

## Did I make a math error or is this happening because of different rounding methods?

„Money accumulates in a fund at an effective annual interest rate of i during the first 5 years, and at an effective annual interest rate of 2i thereafter.

A deposit of 1 is made into the fund at time 0. It accumulates to 3.09 at the end of 10 years and to 13.62 at the end of 20 years. What is the value of the deposit at the end of 7 years?“

The solution in the book sets up two equations:

(1+i)^5 * (1+2i)^5=3.09
(1+i)^5 * (1+2i)^15=13.62

And divides the second by the first to get (1+2i)^10 = 13.62/3.09 = 4.407767 and solves i=.079952

My method was to just use the first equation:

(1+i)^5 * (1+2i)^5=3.09

(1+i) * (1+2i)=3.09^(1/5) etc….expand the quadratic and solve i=.0801

I am using a calculator with display truncated after 4 decimal points but I was under the impression that the internal rounding was identical regardless of display. The fact that my i=.0801 and not .0800 makes me wonder if the way I solved the problem was not mathematically sound. I am pretty sure its due to rounding but the odd method used by the book coupled with the fact that, if you do the problem my way, there is needless information in the problem makes me wonder. Any input is appreciated. I am not very far in math in college so I am always second guessing myself.

What you did is correct, as far as it goes.
All the difficulties stem from the fact that they used numbers rounded to two decimals.

You are correct to observe that the second equation is redundant.

The real answer to this is that i = 0.08 (exactly).

Note that (1.08)^5 * (1.16)^5 = 3.08609097 → rounded to 3.09
right away there is rounding error introduced.
It’s small, but it matters.

If you then solve, as you did using just that equation,
you get 8.0095% because the 10 year number (3.09) is a little too high.

They then used that 3.09 as a divisor, which means their number
4.407767 is too low. Hence their result is just under .08

So I say, your answer is a little bit wrong, it is too high.
Their answer is wrong, too, it is a little too low.

So what do you say you just split the difference, and call it 0.08 ?

In any case, they are not asking for the interest rate, but the value after 7 years.
No matter which of the numbers you use, since they are so close,
the result of that calculation (especially when rounded to 2 decimals)
will be either the same, or be off by no more than .01

Also, if you don’t round to two decimals their method comes out:
(1.08)^5 * (1.16)^15 = 13.61409
13.61409 / 3.08609097 = 4.41143508
If you take that (instead of 4.407767) to the 1/10 you get 2i = .16 and i = .08

Ok. So I have this question on this worksheet and I just can’t get it. It says, „What are the sums on of all of the first 500 counting numbers (1+2+3+4……..498+499+500)?“ and I have a button on my calculator that can multiply all of those number but I can’t add them and I tried to add 1-10 which is 55 and multiply it by 50 (10 times 50 = 500) but it was like 2750 or something which is way too low considering you have to add up all of the 100-400’s and 500.
Anyway, the next question is „How about just the odds (1+3+5+7…..495+497+499)?“ Can someone tell me the answers then tell me how you got them so I can understand and not get tons of points taken off of my homework??? (there are only 5 questions so each question is 20 points…yikes…)

thanks so much for your help!!!

Wow thats hard for a 7th grader?
Okay let me try..
I got 6,500..
110+110= 220 [20-40]
220+220=440 [40-80]
440+440
and so on..
I think its like that if its not…I hope this doesnt confuse you fromteh real way to do it..

Ok. So I have this question on this worksheet and I just can’t get it. It says, „What are the sums on of all of the first 500 counting numbers (1+2+3+4……..498+499+500)?“ and I have a button on my calculator that can multiply all of those number but I can’t add them and I tried to add 1-10 which is 55 and multiply it by 50 (10 times 50 = 500) but it was like 2750 or something which is way too low considering you have to add up all of the 100-400’s and 500.
Anyway, the next question is „How about just the odds (1+3+5+7…..495+497+499)?“ Can someone tell me the answers then tell me how you got them so I can understand and not get tons of points taken off of my homework??? (there are only 5 questions so each question is 20 points…yikes…)

thanks so much for your help!!!

Take the first number and add it to the last number:
1+500=501
Now take the second number and add it to the second to last number:
2+499=501

No matter which number you take if you add it to the corresponding number at the end you will get 501 because it will add a certain amount and then subtract a certain all the time
So if you do actually pair up all the numbers you will get 250 pairs
so 250×501=125250

For odds it’s the same thing
1+499=500
3+497=500
5+495=500

so because you have 1/2 the amount of pairs (odd numbers only) you do 125×500=62500