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Question Number 85546 by TawaTawa1 last updated on 22/Mar/20

Commented by TawaTawa1 last updated on 23/Mar/20

Given that the sum, S,  of a geometric series with a common  ratio  4  is  14,450. Calculate the value of the starting value  of the series if it is an integer and lies between 100 and 500.  Does your answer agree with output of the formular for the  sum of a geometric series (given below)?. Show your workings  out bearing in mind that you camnot use the formular to find  the value of a.                                            S   =   ((a(r^n   −  1))/(r  −  1))

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum},\:\mathrm{S},\:\:\mathrm{of}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{series}\:\mathrm{with}\:\mathrm{a}\:\mathrm{common} \\ $$$$\mathrm{ratio}\:\:\mathrm{4}\:\:\mathrm{is}\:\:\mathrm{14},\mathrm{450}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{starting}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\:\mathrm{and}\:\mathrm{lies}\:\mathrm{between}\:\mathrm{100}\:\mathrm{and}\:\mathrm{500}. \\ $$$$\mathrm{Does}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{agree}\:\mathrm{with}\:\mathrm{output}\:\mathrm{of}\:\mathrm{the}\:\mathrm{formular}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{series}\:\left(\mathrm{given}\:\mathrm{below}\right)?.\:\mathrm{Show}\:\mathrm{your}\:\mathrm{workings} \\ $$$$\mathrm{out}\:\mathrm{bearing}\:\mathrm{in}\:\mathrm{mind}\:\mathrm{that}\:\mathrm{you}\:\mathrm{camnot}\:\mathrm{use}\:\mathrm{the}\:\mathrm{formular}\:\mathrm{to}\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{S}\:\:\:=\:\:\:\frac{\mathrm{a}\left(\mathrm{r}^{\mathrm{n}} \:\:−\:\:\mathrm{1}\right)}{\mathrm{r}\:\:−\:\:\mathrm{1}} \\ $$

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