Question

Find the sum of the first 8 terms of the sequence. Show all work for full credit.

1, -3, -7, -11, ...

Answer 1

Have you studies Arithmetic sequences or progressions?

Answer 2

@katherineekc ??

Answer 3

kinda yeah, im just kinda comfused

Answer 4

Let's find the common difference between the terms
-3-(1)=-4
-7-(-3)=-3+3=-4
So it's an Arithmetic Sequence
common difference= -4
\[a_0=1\\\ \text{First term}\]
Do you get this?

Answer 5

okay, yes i get that!

Answer 6

We need to find the 8 th term
nth term is given as
\[a_n=a_1+(n-1)d\]
n=8, d =-4 (common difference)
\[a_8=a_1+(8-1)\times d\]
\[a_8=1+7\times (-4)\]
Can you find the value of a_8

Answer 7

@katherineekc

Answer 8

- 32 ?

Answer 9

\[a_8=1-28\]
Now find the value of 8th term

Answer 10

-27?

Answer 11

yes now sum of first 8 terms is
\[S=\frac {n}{2}\times (a_1+a_8)\]
n=8
\[a_1=1\]
\[a_8=-27\]
Just simple calculation now, can you do it?

Answer 12

i believe so yes ..

Answer 13

Could you find the value? take your time :)

Answer 14

what would the n value b .. just 1?

Answer 15

n=8

Answer 16

oh duh sorry.. h.o

Answer 17

is it -104?

Answer 18

correct :)

Answer 19

ok:) thank you so much!!!

Answer 20

i hate to be a bother, but do you know how to do this problem?
Write the sum using summation notation, assuming the suggested pattern continues.

25 + 36 + 49 + 64 + ... + n2 + ...