Odpowiedź:
an=2n+1
an=2n+1n=9
an=2n+1n=9an=19
Szczegółowe wyjaśnienie:
a1 = 3
r = 2
Sn = 99
[tex]an = a1 + (n - 1) \times r \\ an = 3 + (n - 1) \times 2 \\ an = 3 + 2n - 2 \\ an = 2n + 1[/tex]
[tex]sn = \frac{a1 + an}{2} \times n = 99 \\ \frac{3 + 2n + 1}{2} \times n = 99 \\ \frac{4 + 2n}{2} \times n = 99 \\ (2 + n)n = 99 \\ {n}^{2} + 2n - 99 = 0 \\ delta = {b}^{2} - 4ac \\ delta = 4 - 4( - 99) = 4 + 396 = 400 \\ \sqrt{delta} = 20 \\ n > 0 \\ n = \frac{ - 2 + 20}{2} = 9 \\ an = 2n + 1 \\ an = 2 \times 9 + 1 = 19[/tex]
