Question

calcule a soma dos n primeiros termos da PA (6, 10, 14, 18, ...).

Answer 1

Resposta:

$P.A. = (6,10,14,18,...) \\ \\ \bf Termo \: geral \: da \: P.A. : \\ \\ \large \boxed{ \bf \: an = a1 + (n - 1)r} \\ \\ \boxed{ a1 = 6 }\\ \\ r = 10 - 6 \\ \boxed{ r = 4} \\ \\ an = 6 + (n - 1)4 \\ \\ an = 6 + 4n - 4 \\ \\ \large \boxed{ \bf \: an = 4n + 2} \\ \\ \bf Soma \: do \: n \: primeiros \: termos : \\ \\ \Large \boxed{ \bf \: Sn = \frac{(a1 + an)n}{2} } \\ \\ Sn = \frac{(6 + 4n + 2)n}{2} \\ \\ Sn = \frac{(4n + 8)n}{2} \\ \\ Sn = \frac{4 {n}^{2} + 8n }{2} \\ \\ \Large \boxed{ \green{ \bf \: Sn = 2 {n}^{2} + 4n}} \\ \\ \Large \boxed{ \underline{ \blue{ \bf \: Bons \: Estudos!} \: \bf \: 19/05/2021}}$