Question

Ana started off her penny collection with 1 penny. She then adds 5 pennies to her penny collection each day.
how could you change the above scenario to make it a geometric series rather than an arithmetic series?
Using the answer, how many pennies would ana have in total after 10 days?
show and use the formula to calculate
show all work

pls help i struggle.. thank you

Answer 1

well the one in the problem is arithmetic because it adds the same # of pennies every single day

to change this to a geometric series you would just change the addition to multiplication. so, instead of adding 5 pennies per day, you could simply multiply by 5

the last part of the problem isn't really clear whether they want the original, or the geometric one, so I'll do both:

Answer 2

the sum of an arithmetic series is

(n/2) (2 a_1 + (n-1)d )
where n is the number of terms in the series, a_1 is the first term, and d is the common difference

in your problem, n is 10, a_1 is 1, and d is 5

Answer 3

using the geometric sum formula,

a_1* (1-r^n)/(1-r)
where a_1 is 1, r is 5, and n is 10

Answer 4

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
using the geometric sum formula,

a_1* (1-r^n)/(1-r)
where a_1 is 1, r is 5, and n is 10
\(\color{#0cbb34}{\text{End of Quote}}\)



Thank you ! Ill for sure use these as some notes to look over!