Question

Quantos termos tem a P.A (120,125,...,3250)?

Answer 1

Encontrar a razão da PA

r = a2 - a1
 r = 125 - 120  
r  =  5

===

an = a1 + ( n -1) . r
3250 = 120 + (  n  -1) . 5
3250 = 120 + 5n - 5
3250 = 115 + 5n
3135 = 5n  
n = 627


PA com 627 termos.

Answer 2

Boa noite!

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$\mathbf{R}\Rightarrow\textit{a2-a1}\Rightarrow\textit{125-120} = \textit{5}$
$\textit{An}=\textit{3250}$
$\textit{A1}=\textup{120}$

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$\textit{An}=\textit{A1+(n-1).r}$
$\textit{3250} = \textit{120+(n-1).5}$
$\textit{3250} = \textit{120+5n-5}$
$\textit{3250-5n} = \textit{120-5}$
$\textit{3250-5n} = \textit{115}$
$\textit{-5n} = \textit{115-3250}$
$\textit{-5n} = \textit{-3135}(-1)$
$\textit{5n} = \textit{3135}$
$\textit{n} = \frac{3135}{5}$
$\textit{n} = \boxed{\boxed{627}}$

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Att;Guilherme Lima