Question

ME AJUDEM POR FAVOR!!!

*Progressão Aritmética*

Calcule o valor das somas a seguir:​

Answer 1

Resposta:

Explicação passo a passo:

Aplicando a fórmula, resolvemos:

a)

$a_{n} =a_{1} +(n-1)r\\302=5+(n-1)3\\302=5+3n-3\\302=2+3n\\300=3n\\n=100\\\\\\S_{n} =\frac{(a_{1} +a_{n})n }{2} \\\\S_{100} =\frac{(5 +302)100}{2} \\\\S_{100} =307\:.\:50\\\\S_{100} =307\:.\:50\\\\S_{100} =15350$

b)

$a_{n} =a_{1} +(n-1)r\\570=2+(n-1)8\\570=2+8n-8\\570=-6+8n\\576=8n\\n=72\\\\\\S_{n} =\frac{(a_{1} +a_{n})n }{2} \\\\S_{72} =\frac{(2+570)72}{2} \\\\S_{72} =572\:.\:36\\\\S_{72} =20592$

c)

$a_{n} =a_{1} +(n-1)r\\50=-20+(n-1)7\\50=-20+7n-7\\50=-13+7n\\63=7n\\n=9\\\\\\S_{n} =\frac{(a_{1} +a_{n})n }{2} \\\\S_{9} =\frac{(-20+50)9}{2} \\\\S_{9} =\frac{30\:.\:9}{2} \\\\S_{9}=15\:.\:9\\\\S_{9}=135$

Espero ter ajudado!

Desculpe qualquer erro.