Question

Um atleta corre 400 metros a mais que no dia anterior. Ao final de 11 dias ele percorre um total de 35.200 metros. O número de metro que ele correu no último dia foi igual a?

Answer 1

a1 = x

a2 = x + 400

r = 400 ***

a11  =  a1 + 10r

a11  = x + 10(400 )

a11  = x + 4 000  ****

S11  = 35 200

S11  = (  a1 + a11) * 11/2

35 200  = [ x + ( x + 4000)] . 5.5

35 200/5.5 =  ( 2x + 4 000 )

6 400  = 2x + 4 000

6400 - 4000  = 2x

2x =  2 400

x = 2400/2 =  1 200  ****

a1 = 1 200

a2 = 1200 + 400  = 1 600

a3 = 1600 + 400  = 2 000

a11 =  a1 + 10 r

a11 = 1200 + 10 ( 400 )

a11  = 1200 + 4 000

a11 = 5 200 ***** resposta

PROVA

( a1 + a11 ) . 11/2  = 35 200

( 1200 + 5200 ) . 5,5 = 35 200

6 400 * 5.5 = 35 200

35 200  = 35 200  confere  ****

se ajudei p.f vote  com estrelas

Answer 2

$\sf \sf \displaystyle 35200=\left(a1+an\right)\frac{11}{2}\\\\\\\sf 35200=\left(a\cdot \:1+an\right)\frac{11}{2}\\\\\\\sf \left(a\cdot \:1+an\right)\frac{11}{2}=35200\\\\\\\sf 2\left(a\cdot \:1+an\right)\frac{11}{2}=35200\cdot \:2\\\\\\\sf 11\left(a+an\right)=70400\\\\\\\sf \frac{11\left(a+an\right)}{11}=\frac{70400}{11}\\\\\\\sf a+an=6400\\\\\\\sf a\left(1+n\right)=6400\\\\\\\sf \frac{a\left(1+n\right)}{1+n}=\frac{6400}{1+n}\\\\\\\to \boxed{\boxed{\sf a=6400}}$

$\tt \tt an=\left(6400-an\right)+\left(11-1\right)\cdot 400\\\\\\\tt an=6400-an+\left(11-1\right)\cdot \:400\\\\\\\tt an=6400-an+4000\\\\\\\tt an=-an+10400\\\\\\\tt an+an=-an+10400+an\\\\\\\tt 2an=10400\\\\\\\tt \dfrac{2an}{2n}=\dfrac{10400}{2n}\\\\\\\to \boxed{\boxed{\sf a=5200}}$