Question

Me ajuda estou precisando

1) ache a soma dos 50 primeiros termos da P.A finita (10,8,6,...) ?


2) ache o 20° termo da P.A finita (12,8,4,...) ?

Answer 1

$> resolucao \\ \\ \geqslant progressao \: \: aritmetica \\ \\ r = a2 - a1 \\ r = 8 - 10 \\ r = - 2 \\ \\ \\ a50 = a1 + 49r \\ a50 = 10 + 49 \times ( - 2) \\ a50 = 10 + ( - 98) \\ a50 = 10 - 98 \\ a50 = - 88 \\ \\ \\ sn = \frac{(a1 + an)n}{2} \\ \\ sn = \frac{(10 + ( - 88) \: )50}{2} \\ \\ sn = \frac{(10 - 88)50}{2} \\ \\ sn = \frac{ - 78 \times 50}{2} \\ \\ sn = - 78 \times 25 \\ \\ sn = - 1950 \\ \\ \\ = = = = = = = = = = = = = = = = = = = = \\ \\ \\ r = a2 - a1 \\ r = 8 - 12 \\ r = - 4 \\ \\ \\ a20 = a1 + 19r \\ a20 = 12 + 19 \times ( - 4) \\ a20 = 12 + ( - 76) \\ a20 = 12 - 76 \\ a20 = - 64 \\ \\ \\ sn = \frac{(a1 + an)n}{2} \\ \\ sn = \frac{(12 + ( - 64) \: )20}{2} \\ \\ sn = \frac{(12 - 64)20}{2} \\ \\ sn = \frac{ - 52 \times 20}{2} \\ \\ sn = - 52 \times 10 \\ \\ sn = - 520 \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant \geqslant$