Question

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

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

Answer 1

This is an AP with common difference -5 and first term 1..
you know the formula for sum of n terms of an AP?

Answer 2

\[S{n}=\frac{ n }{ 2 }(a _{1}+a_{n})\]

Answer 3

right?

Answer 4

yeah. if you want to use this.. you need to find the twelfth term.. you know the formula for that?

Answer 5

im not sure

Answer 6

formula to find the nth term..

Answer 7

an=a+(n-1)d

Answer 8

so the formula for the nth term of an arithmetic sequence?

Answer 9

where a is the first term, n is the number of terms.. put n=12 and find the twelfth term..

Answer 10

yeah. a_12 = 1 + 11(-5) = 1 - 55 = -54..
so your 12th term is -54..

Answer 11

where did you get -5?

Answer 12

oh wait nevermind i remember

Answer 13

We remark that :
\[-4-1=-5\\
-9-(-4)=-5
\\-14-(-9)=-5\]
The difference between every consecutive terms is -5, so this is an arithmetic progression with first term u_1=1 and the common difference d=-5.
So :
\[S_{12}=u_1+\cdots u_{12}=\frac{12}{2}(2u_1+11d)\]

Answer 14

now you have a_n, a.. and you know n which is 12.. plug all of that in that sum formula..

thats the common differnce..

Answer 15

So S_n = (12/2)*(1 + (-54) = 6*(-53) = -318.. thats your answer.

Answer 16

okay, im not sure i understand fully, but thank you.

Answer 17

Reply back if you have any problems.
You're welcome.