Question

1) Calcule a soma dos treze termos da sequência (8,14,20,... 74,80). Use a fórmula : Sn=(a1+an).n/2.

2) Calcule a soma dos vinte primeiros termos (n=20) da PA (5,9,13,17,21,...) Use as fórmulas : an=a1+(n-1).r e Sn= (a1+an).n/2 "

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Answer 1

Explicação passo-a-passo:

1)

$(8,14,20,...,74,80) \\ a _{1} = 8 \\a_{13} = 80 \\ s_{n} = \dfrac{(a_{1} +a_{n} )n}{2} \ \\ \ \ \: s_{13} = \dfrac{(a_{1} +a_{13} )13}{2} \\ \\ s_{13} = \dfrac{(8 +80 )13}{2} \\ \\ s_{13} = \dfrac{(88)13}{2} \\ \\ s_{13} = 44 \times 13 \\ \\ \LARGE\boxed{ \bf \green{s_{13} = 572}}$

2)

$\blue{n = 20} \\ (5,9,13,17,21,...) \\ a _{n} = a _{1} + (n - 1)r \\ \blue{a _{1} = 5 }\\ r = 9 - 5 \\ \blue{ r = 4 }\\ a _{20} = 5 + (20 - 1)4 \\ \\ a _{20} = 5 + (19)4 \\ \\ a _{20} = 5 + 76 \\ \\ \orange{ a _{20} = 81} \\ \\ s _{n} = \dfrac{(a _{1} + a _{n})n}{2} \\ \\ s _{20} = \dfrac{ (5 + \orange {a _{20}} )20}{2} \\ \\ s _{20} = \dfrac{(5 + 81)20}{2 }\\ \\ s _{20} = \dfrac{(86)20}{2} \\ \\ s _{20} = 86 \times 10 \\ \\ \LARGE \boxed{ \bf \green{s _{20} = 860}} \\ \\ \LARGE \boxed {\bf \blue{ \underline{Bons \: Estudos!}}}$