Finite geometric series: Hi, I want to ask a question, is about... for example, take the sequence 1,2,4,8,... Notice that each number is twice the value of the previous number. So, a number in the sequence can be represented by the function f(n) = 2^n-1. One way to write the sum of the sequence through the 5th number in the sequence is E^5 n-1^2n-1. This equation can also be written as S5 = 2^0 + 2^1+2^2+2^3+2^4. If we multiply this equation by 2, the equation becomes 2(S5) = 2^1+2^2+2^3+2^4+2^5.
What happens if I subtract the two equations and solve for S5? Can I use this information to come up with a way to find any geometric series Sn in the form E^a n-1^bn-1?

Hye ryung is the president of the local chapter of the american medical students association (amsa). she is organizing local outreach and informational meetings. at her first meeting there are five people present (including herself). every month after that her group grows by 5 people. a. how many members are in the group after 6 months? b. the logistics of hosting and feeding her group at meetings was more complicated than expected. the cost of feeding 5 people at her first meeting was $30, for 10 people it was $35, for 15 it was $45, and after 6 months all of the costs had added up to $100. write a function to model the cost with the number of people attending meetings. c. what connections can you make between the linear growth of the group’s membership and the increasing costs of running meetings?

Agarden consists of an apple tree, a pear tree, cauliflowers, and heads of cabbage. there are 40 vegetables in the garden. 24 of them are cauliflowers. what is the ratio of the number of cauliflowers to the number of heads of cabbage?

Create a question with this scenario you could ask that could be answered only by graphing or using logarithm. david estimated he had about 20 fish in his pond. a year later, there were about 1.5 times as many fish. the year after that, the number of fish increased by a factor of 1.5 again. the number of fish is modeled by f(x)=20(1.5)^x.