Question

I need an explanation: What is the sum of a 6–term geometric series if the first term is 6 and the last term is 1,000,842?

Answer 1

?

Answer 2

Divide 1000842 by 6 and take the 5th root of the quotient.

Answer 3

Let p = the common ratio, then first term is a0, and the 6th term is ar^5.
So a0 r^5/a0=r^5. The fifth-root of the quotient is therefore the common ratio (=7)

Answer 4

correction r=common ratio.

Answer 5

okay

Answer 6

thx

Answer 7

a(sub n)=a(sub 1)r^(n-1)

Answer 8

You're welcome! But see what LivyLou has to say. She has been working on your problem for quite a while.

Answer 9

Oops yeah I took awhile because I was checking to see if I was giving the right formula

Answer 10

ok thanks

Answer 11

im confused

Answer 12

how so?

Answer 13

what do i put into the formula

Answer 14

i know the common ratio is 7 but how do u get that

Answer 15

I'm actually not sure either. I reread the question and I don't think the formula I gave helps. sorry

Answer 16

its okay

Answer 17

@jittcam @LivyLou
The first term can be considered as a(1), and the second term as a(2), ... the nth term is a(n).
We know that there is a common ratio, r, such that
\[ r=a_2 / a_1 = a_3 / a_2 = .... \]
So
\[ a_0*r = a_1 \]
\[ a_0*r^2 = a_2 \]
\[ a_0*r^3 = a_3 \]
...
\[ a_0*r^6 = a_6 \]
Thus
\[ \frac{a_6}{a_1} = \frac{a_0 r^6}{a_0 r} = r^5 \]
In our case,
\[ \frac{a_6 }{a_1} = \frac{1000842}{6} = r^5 \]
Therefore
\[ r=166807^{1/5} = 7\]

Hope this helps.

Answer 18

when i put 166807^{1/5} in my calculator i get 11 not 7