an infinite geometric series has a sum of 2020. a new series, obtained by squaring each term of the original series, has 10 times the sum of the original series. what is the common ratio of the original series

2020 ==F / [1 - r],

20200=F^2/[1 - r^2], solve for F, r

Divide the 2nd by the first:

F ==4040 / 203 - this is the first term of the original sequence

r ==201 / 203 - this is the common ratio of the original sequence.