Question

1 ) verifique o valor do décimo quarto termo (a14) da sequência numérica (2,7,12,17,...) " Use a fórmula : an=a1+(n-1).r " ​

2) Calcule a soma dos termos da sequência (15,23,31,39,47,55,63,71,79,87) . Use a fórmula : Sn= (a1+an).n/2.

Answer 1

Explicação passo-a-passo:

1)

(2,7,12,17,...)

$r = 7 - 2 \\ \pink{ r = 5} \\ \pink{a _{1} = 2} \\ \\ a _{n} = a _{1} + (n - 1)r \\ \\ a _{n} = 2 + (n - 1)5 \\ \\ a _{n} = \orange{ 2 }+ 5n \orange{- 5} \\ \ \boxed{\bf{a _{n} = 5n - 1} \: termo \: geral} \\ \\ a _{14} = 5(14) - 1 \\ \\ a _{14} = 70 - 1 \\ \\ \LARGE\boxed{ \bf \green{{ a _{14} = 69}}}$

2)

$(15,23,31,39,47,55,63,71,79,87) \\ \\ s _{n} = \dfrac{(a _{1} + a _{n} )n}{2} \\ \\ s_{10} = \dfrac{( a _{1} \: +s _{10} )10}{2} \\ \\ s_{10} = \dfrac{(15 + 87)10}{2} \\ \\ s _{10} = \dfrac{(102)10}{2} \\ \\ s _{10} = \dfrac{1020}{2} \\ \\ \LARGE\boxed{ \bf \green{s _{10} = 510}} \\ \\ \LARGE \boxed{ \bf \blue{ \underline{Bons \: Estudos!}}}$