Arrange these numbers from least to greatest: 2 over 5 comma text end text − 3 over 7 comma text end text 2 over 3.
2 over 5 comma text end text − 3 over 7 comma text end text 2 over 3
− 3 over 7 comma text end text 2 over 5 comma text end text 2 over 3
− 3 over 7 comma text end text 2 over 3 comma text end text 2 over 5
2 over 5 comma text end text 2 over 3 comma text end text text end text − 3 over 7
my best interpretation of this is that you're given a geometric progression consisting of terms, the first of which is and the last of which is . (so we don't actually know right away how many terms there are.) the common ratio between terms is . you want to find the sum of all terms.
in a geometric progression, the -th term is determined by the previous term according to
starting with , we find
and so on. the general pattern for the -th term is then
the last term in the sequence is , so
the sum of these terms is given by
with and , we get a sum of
let n represent the number
twice the number =2n
4 times the number = 4n
given that twice the number is atleast 3 less than four times the number
algebraically this can be written as
we can add 3 to both sides
so n should be atleast 1.5
if n is natural number or integer then least value of n is 2.