Question

Find the sum of the first 12 terms of the sequence. Show all work for full credit.

1, -4, -9, -14, . . .

Answer 1

is it a random sequence? an arithmetic sequence? a geometric sequence? a sequence generated by a function?

the information is rather too vague to determine a solution. I can make a function that only hits those 4 points and is zero for everything else. hence the term"sequence" is not enough to go on.

Answer 2

I just copied and pasted the question... I think it might be an arithmetic sequence but im not sure. Im in the chapter about series and summation if that helps.

The reason I think it would be arithmetic is because the sequence decreases by 5 but im probably wrong....

Answer 3

no, your on the right track, its just that the question makes you assume it, instead of telling you our right.

the thing is, i can make a function that just generates those 4 numbers, and everything else is zero ... so making you assume it to be arithmetic is not fair.

Answer 4

yup decrease by 5 good

Answer 5

so, if you assume that it decreases by 5 each time, what are the first 12 terms?

Answer 6

would i include the ones given??

Answer 7

of course, those are the first 4 terms

Answer 8

This is what is known as an arithmetic sequence. That is you add the same thing to number you have to get the next number in the sequence. If you look at this you keep adding -5 to a term to get the next term

There is a formula for the sum of the terms of a sequence.
If a is the first term of the sequence ( here its 1) and d is the common difference( what you add to one term to get the next, here its -5) then if you want to sum n terms ( n is just a number , here its 12)
Sum = n/2[2a +(n-1)d ]
= 12/2[2*1 + (12-1)*(-5)]
= 6 [2 +11*(-5)}
= 6[2 - 55]
= 6 * -53
= ?

Answer 9

alright. so an=1
a1=-4
a2=-9
a3=-14
a4=-19
a5=-24
a6=-29
a7=-34
a8=-39
a9=-44
a10=-49
a11=-54
a12=-59

Answer 10

or would a1=1 and so on making the 12th term -54?

Answer 11

for n >= 0

\[f(n)=\frac12(1+\frac{n-3.5}{|n-3.5|})(1-5n)\]

http://www.wolframalpha.com/input/?i=table+%5B%281-5%28n-1%29%29%281-%28n-1-3.5%29%2F%7Cn-1-3.5%7C%29%2F2%2C%7Bn%2C12%7D%5D

Answer 12

i cant do anything with this lag ...

Answer 13

me???

Answer 14

did you get my last post??

Answer 15

it starts with 1

Answer 16

so a_n would be 1 or a_1 would be 1?

Answer 17

in your case a_0 = 1 since you already defined the others starting at a_1 :)

Answer 18

a0 = 1
a1=-4
a2=-9
a3=-14
a4=-19
a5=-24
a6=-29
a7=-34
a8=-39
a9=-44
a10=-49
a11=-54
---------- first 12 terms
a12=-59

Answer 19

you know how to add them up?

Answer 20

Oh alright! awesome! Thank you so much for your help! I just wish the question was more clear and yes thats what i posted when you asked me to name the first 12 terms!

Answer 21

if they simply want you to add them, then you can combine them one by one; its an effective method but not always practical.

Answer 22

yeah... I hope this is what they were asking for. Thank you again!!

Answer 23

good luck

Answer 24

:)