Question

Calcule a soma dos vinte primeiros termos da PA (0,15,0,40,0,65,0,9,..)

Answer 1

Resposta:

a soma de dos 20 primeiros ternos dão 51,5

Explicação passo-a-passo:

$r = a2 - a1 \\ r = 0 .40 - 0.15 = 0.25 \ \\ r = 0.25 \\ sn = \frac{(a1 + a2)n}{2 \\ } = \frac{(0.15 + 5) \times 20}{2} = 5.15 \times 10 = \\ sn = 51.5 \\ a2 = a1 + (n - 1)r \\ a2 = 0.15 + (20 - 1) \times 0.25 \\ a2 = 0.15 + 19 \times 0.25 = 5$

Answer 2

Resposta:

$S_{20} =50,5$

Explicação passo a passo:

$a_{1} =0,15=\frac{15}{100} =\frac{3}{20} \\\\a_{2} =0,4=\frac{4}{10} =\frac{2}{5}=\frac{8}{20} \\\\r=a_{2} -a_{1} =\frac{8}{20} -\frac{3}{20} =\frac{8-3}{20} =\frac{5}{20} =\frac{1}{4} \\\\n=20\\\\a_{n} =\ ?\\\\S_{n}=\ ?? \\\\\\\\a_{n} =a_{1} +(n-1)\times r\\\\a_{20} =\frac{3}{20} +(20-1)\times \frac{1}{4} \\\\a_{20} =\frac{3}{20} +19\times \frac{1}{4} \\\\a_{20} =\frac{3}{20} + \frac{19}{4} \\\\a_{20} =\frac{3}{20} + \frac{95}{20} \\\\a_{20} =\frac{3+95}{20}$

$a_{20} =\frac{98}{20} \\\\\\\\S_{n} =\frac{(a_{1} +a_{n} )\times n}{2} \\\\S_{20} =\frac{(\frac{3}{20} +\frac{98}{20} )\times 20}{2} \\\\S_{20} =\frac{(\frac{3+98}{20} )\times 20}{2} \\\\S_{20} =\frac{(\frac{101}{20} )\times 20}{2} \\\\S_{20} =\frac{101}{2} \\\\S_{20} =\frac{100+1}{2} \\\\S_{20} =\frac{100}{2} + \frac{1}{2} \\\\S_{20} =50+0,5\\\\\bold{S_{20} =50,5}$