The second and fourth term of a geometric series is 100 and 225 respectively. Find the common ratio and first term of the series. Round your answer to 2 d.p if necessary
Formula for a Geometric series for term n = arn , where a = the first term and r = common ratio.Therefore, with the information given we can write that ar2 = 100 and ar4 = 225 , where a and r are the constants we're trying to find
By dividing these two equations together we get that ar4 / ar2 = 225 / 100this can then be simplified to r2 = 2.25, which can be square rooted to show that r = 1.5
After working this out, when can sub r=1.5 back into one of the equations for the two terms given, for example ar2 = 100, to get that a(1.5)2 = 100 by dividing by 1.52 on both sides we can show that a = 44.44 to 2 d.p
