Question

ache a soma dos termos da p.a(33,36,...345)

Answer 1

Boa noite!

Dados;

A1 → 33

N → ?

An → 345

R → a2-a1 → 36-33 = 3

__________________

An=a1+(n-1)·r

345=33+(n-1)·3

345=33+3n-3

-3n=33-3-345

-3n=30-345

-3n=-315

n=-315/-3

n=105

______________

$\textit{Sn}=\frac{\mathrm{(A1+An).n}}{\mathrm{2}}$

$\textit{S105}=\frac{\mathrm{(33+345).105}}{\mathrm{2}}$

$\textit{S105}=\frac{\mathrm{378.105}}{\mathrm{2}}$

$\textit{S105}=\frac{\mathrm{39690}}{\mathrm{2}}$

$\mathbf{S105}=\boxed{19845}$

Att;Guilherme Lima

Answer 2

An= 345

A₁= 33

r= 3

An= A₁+(n-1)3

345= 33+(n-1)3

345-33= (n-1)3

312= (n-1)3

n-1= 312/3

n= 104+1

n= 105

Fórmula da soma de n  termos → Sn= (A₁+An)n/2

Sn= (33+345)105/2

Sn= 378*105/2

Sn= 189*105

Sn= 19845

Resposta → A soma dos 105 termos  desta PA resultam em 19.845