Can someone explain the process of solving this problem?
-What is the common difference of a 43-term arithmetic sequence where the first term is -13 and the sum is 9,374?

Question

Can someone explain the process of solving this problem?
-What is the common difference of a 43-term arithmetic sequence where the first term is -13 and the sum is 9,374?

amistre64 · Answer

id start with the formula for the sum of an arith progression

amistre64 · Answer

each term can be written in terms of the first term ... lots of terms in this sentence

amistre64 · Answer

can you recall any formulas for these?

anonymous · Answer

no :/ i haven't learned these

amistre64 · Answer

they should be found in your material; you may want to review your material so that you have at least a basic knowledge required to proceed

anonymous · Answer

it's an online course, so i only take quizzes i don't have a teacher or anything, i basically have to look up everything online.

amistre64 · Answer

those formulas can be found online as well.  we will need them in order to move ahead.  we could develop them if need be, but thats only an option if you truely want to learn how they work ...

anonymous · Answer

so a is the first term and d is the common difference in the formulaxn = a^sub x + d(n-1)

amistre64 · Answer

thats a good start, alittle rough, but good enough to work on

amistre64 · Answer

the sum of an arith progression can be calculated by adding the first and last term, and multiply the result by half the number of terms that there are.

amistre64 · Answer

a1 + a1 + d(n-1) = 2a1 + d(n-1)

we know there are 43 terms and that it has to equal that given amount

anonymous · Answer

okay, how to i find the last term then?

amistre64 · Answer

the last term is not that important to know since it can be defined by the first term

anonymous · Answer

all i have is-13x+d(n-1) so I'm confused how to apply the formula to get what you have.

amistre64 · Answer

the first term is:$$a_1$$the last terms is:
$$a_n=a_1+d(n-1)$$
adding these together we get$$a_1+a_1+d(n-1)=\color{red}{2a_1+d(n-1)}$$

anonymous · Answer

ahhhhh okay!

amistre64 · Answer

therefore the sum is defined to be:$$\frac n2(first+last)$$
$$9374=\frac{43~(\color{red}{2(-13)+d(43-1)})}{2}$$
we now everything in that except for d,

amistre64 · Answer

im sure you know how to do the algebra for d right ...

anonymous · Answer

yep! ill let you know what i get!

anonymous · Answer

i got -8.71 , but my answer choices are 

1)	11
2)	11.5
3)	12
4)	12.5

anonymous · Answer

i didn't dived by 2 ahh hold on

amistre64 · Answer

lol, lets unravel the d$$9374=\frac{43~(\color{red}{2(-13)+d(43-1)})}{2}$$
$$2(9374)=43~(\color{red}{-2(13)+d(42)})$$
$$\frac{2(9374)}{43}=\color{red}{-2(13)+d(42)}$$
$$\frac{2(9374)}{43}+2(13)=\color{red}{d(42)}$$
$$\frac{\frac{2(9374)}{43}+2(13)}{42}=\color{red}{d}$$

anonymous · Answer

but then i got -17.42 :/

amistre64 · Answer

that will result in one of the options ....

amistre64 · Answer

or if the mathing is tricking you up; we know the formula; so plug in the options to see what fits

amistre64 · Answer

does...
$$9374=\frac{43~(\color{red}{2(-13)+\color{green}{11}(43-1)})}{2}$$
or
$$9374=\frac{43~(\color{red}{2(-13)+\color{green}{11.5}(43-1)})}{2}$$
or etc ...

anonymous · Answer

9.76. WRONG AGAIN. sorry i am very very bad with math.

amistre64 · Answer

:) if your using a calculator, then its prolly trying to interpret your input keys ... 9374=43(2(-13)+d(43-1))/2 http://www.wolframalpha.com/input/?i=9374%3D43%282%28-13%29%2Bd%2843-1%29%29%2F2

anonymous · Answer

AH WOW....thank you that makes a lot of sense.

amistre64 · Answer

youre welcome, and good luck :)