Question Number 178467 by mokys last updated on 16/Oct/22
$${find}\:{n}^{{th}\:} {terms}\:{of}\:\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{11},\mathrm{13},\mathrm{15},\mathrm{17},. \\ $$
Answered by Frix last updated on 16/Oct/22
![a_n =−((41n^7 )/(5040))+((37n^6 )/(144))−((2381n^5 )/(720))+((3211n^4 )/(144))−((15173n^3 )/(180))+((3185n^2 )/(18))−((39247n)/(210))+77 [btw. given a_7 =15 is not a prime number]](https://www.tinkutara.com/question/Q178473.png)
$${a}_{{n}} =−\frac{\mathrm{41}{n}^{\mathrm{7}} }{\mathrm{5040}}+\frac{\mathrm{37}{n}^{\mathrm{6}} }{\mathrm{144}}−\frac{\mathrm{2381}{n}^{\mathrm{5}} }{\mathrm{720}}+\frac{\mathrm{3211}{n}^{\mathrm{4}} }{\mathrm{144}}−\frac{\mathrm{15173}{n}^{\mathrm{3}} }{\mathrm{180}}+\frac{\mathrm{3185}{n}^{\mathrm{2}} }{\mathrm{18}}−\frac{\mathrm{39247}{n}}{\mathrm{210}}+\mathrm{77} \\ $$$$\left[\mathrm{btw}.\:\mathrm{given}\:{a}_{\mathrm{7}} =\mathrm{15}\:\mathrm{is}\:\mathrm{not}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\right] \\ $$