Question

Find the sum of the first 12 terms of the sequence.

1, -4, -9, -14, . . .
I have no idea how to approach this.

Answer 1

is the sequence arithmetic, or geometric, or other?

Answer 2

sequence arithmetic

Answer 3

good, then it will have the general structure of:\[a_n=a_1+d(n-1)\]right?

Answer 4

yes. I am just not sure how to work that structure into the given info.

Answer 5

well, we are given a1,a2,a3, and a4 values, we just needed to determine "d" and we are pretty much set for the first part. so rearrange the general setup to solve for d\[\frac{a_n-a_1}{n-1}=d\]
we know the value of a1=1 and the value of say, a2 = -4 sooo
what do you determine the value of d is?

Answer 6

How would i know 'n'?

Answer 7

notice that when we n=2 the formula simply states that "d" is the difference between the first 2 numbers:\[\frac{a_2-a_1}{2-1}=a_2-a_1=d\]

Answer 8

n is the "nth" number in the sequence

Answer 9

so d =-5

Answer 10

think of "n" as a placeholder.

and yes, d=-5 :)

Answer 11

soo\[a_n=a_1-5(n-1)~:~a_1=1\]
\[a_n=1-5(n-1)\]now what would the 12th term be? let n=12

Answer 12

a12=54
so would i just find each term up to the 12th and then add them all?

Answer 13

well, -54

you can do that method if you want to. or you can work some simpler methods. they all give youthe same results

Answer 14

ok, thank you so much! I think i'm beginning to understand this now :)

Answer 15

youre welcome. let me know what your sum is, and i can dbl chk it if you want

Answer 16

a_n = 1-5(n-1)
= 1 -5n +5
= 6 - 5n

a1 = 6 - 5(1)
a2 = 6 - 5(2)
a3 = 6 - 5(3)
a4 = 6 - 5(4)
...
a12 = 6 - 5(12)
----------------
sum: 12(6) - 5(1+2+3+4+5+...+12)

72 - 5(13)(6)

72 - 30(13)

72 - 390 is what i get

Answer 17

so i got -318 with simply adding it, next time i will try your way. it seems quicker

Answer 18

:) -318 is what i got too

Answer 19

thanks again for your help!

Answer 20

good luck ;)