Question

3. What is the sum of a 6-term geometric sequence if the first term is 11, the last term is -11,264 and the common ratio is -4?

Answer 1

Sum of a GP = a(r^n - 1) / ( r-1)
a = first term = 11
n = number of terms
r = common ratio

Answer 2

HOW DO I DO THIS ?

Answer 3

Substite the values of a = 11, n = 6, r = -4 into the equation:
Sum of a GP = a(r^n - 1) / ( r-1)

Do let me know if you have any issues.

Answer 4

Sorry, an alternate equation would be:
Sum of GP = a(1-r^n) / (1-r)

Didn't notice the negative r there.

Answer 5

can you please take me step by step or can I just see the work on how to do this ?

Answer 6

@dauspex

Answer 7

Okay ...as written above your equation looks like

\[Sum_n = a\frac{ 1 - r^n }{ 1 - r }\]

'a' represents your first term (in your case 11)
'r' represents your common ratio (-4 in your case)
and 'n' represents the number of terms in your sequence (6 in your case)

So what your equation is going to look like after substituting all those values in...will be

\[Sum_6 = 11\frac{ 1 - (-4)^6 }{ 1 - (-4) }\]

So first...lets do that exponent....what is -4^6?

Answer 8

Well here I'll continue the steps so you can see it...

okay well

\[-4^6 = 4096\]

so we have

\[Sum_6 = 11\frac{ 1 - 4096 }{ 1 + 4 }\]

*on the bottom...notice how 1 - (-4) went to 1 + 4*

So now lets do the arithmetic

\[Sum_6 = 11\frac{ -4095 }{ 5 }\]

And finally lets do the mulitplication

\[Sum_6 = \frac{ 11 \times -4095 }{ 5 }\]

\[Sum_6 = \frac{ -45045 }{ 5 }\]

\[Sum_6 = -9009\]

And that is how you do it

Answer 9

Hope that's understandable @koreanhugg