What is the sum of a 6–term geometric series if the first term is 6 and the last term is 196,608?

Question

anonymous · Answer

Gauss' formula again:$$s=\frac{6}{2}(6+196608)=589842$$

anonymous · Answer

Do you want to see how this Gauss formula works, or why it works I should write?

anonymous · Answer

i tried that but thats for arithmitic series, this is a geometric series

anonymous · Answer

I dont know how to do that formula

anonymous · Answer

ok, sorry; i didn't read closely.

anonymous · Answer

Unless there is more info, this is a two step problem; first we have to find the common ratio, r, then we can use a formula.  i was just checking around to see if there was a formula that i did not know about that did not use r.

(find r on the next post)

anonymous · Answer

explicit definition geometric sequence is$$a _{n}=a _{1}r^{n-1}$$we have all variables except r$$196608=6r^{6-1}$$$$r=8$$(find the sum on the next post)

anonymous · Answer

The formula is $$s=\frac{a _{1}(1-r^n)}{1-r}$$filling-up the formula$$s=\frac{6(1-8^6)}{1-8}=224694$$