Question

What is the sum of the geometric sequence 1, –4, 16, … if there are 7 terms?

Answer 1

do you know the formula?

Answer 2

yes

Answer 3

can you write it please? :)

Answer 4

You can write a geometric sequence like this:
{a, ar, ar^2, ar^3, ar^4...}

Answer 5

All you need to find is the common ratio, which is -4
Explanation:
-4/1 = -4
16/-4 = -4

r would be -4
The first term is 1
So your sequence should look like this
{1, 1*-4, 1*(-4)^2....}

Answer 6

To get the sum, use \[\sum_{a=1}^{7}ar^k\]

Answer 7

\[\LARGE r={a_n\over a_{n-1}}={a_2\over a_1}={-4\over 1}=-4\]

now substitute:
\[\LARGE S_7=a_1\cdot \frac{1-r^{7}}{1-r}\]

Answer 8

How do you make the text bigger? @Kreshnik D:

Answer 9

\[\Huge \text{I DON'T KNOW!}\]
\[\Huge 1+2=3\]

:P use

\LARGE x-2 ...
or \huge 45654
or the one I just used:"
\Huge x-26565445698765435357357357357... :)

Answer 10

Alright thanks :D
\[\huge \sum_{a=1}^{7}ar^k = a(\frac{1-r^7}{1-r})=1(\frac{1-(-4)^7}{1-(-4)})\]

Cool ^^

Answer 11

@zepp which one's better?
\[ \Huge \left( \frac32 \right) \]
\[\Huge (\frac32) \]
??


use:

\left( \frac32 \right)

Answer 12

First one :D

Answer 13

\[\Huge \lim_{x\to \infty}\left[\frac{x^2+2x}{\sqrt{x^7-56x}}\right]\]
this looks cute :) lol

Answer 14

Indeed ;D @Kreshnik