Question

RECOMPENSA: 50 pontos

Gincana da noite

PA (x, 2x + 1, 5x + 3), calcule o centésimo termo (a100).

Boa sorte lksksk​

Answer 1

a + c = 2.b ==> 3termos(a,b,c) em pa

x + 5x+3 = 2.(2x+1)

6x+3 = 4x +2

6x -4x = 2 -3

2x = -1

x = -1/2 (a1) ✓

2x+1=2(-1/2)+1=-1+1=0 (a2). ✓

r = a2-a1= 0 -(-1/2)= 1/2. ✓

a100= a1 +99.r

a100= -1/2 +99(1/2)

a100= -1/2 + 99/2

a100= 98/2

a100= 49 <=====©

Answer 2

Resposta:

$a100 = 49$

Explicação passo-a-passo:

$a1 + a3 = 2a2 \\ x + 5x + 3 = 2(2x + 1) \\ 6x + 3 = 4x + 2\\ 6x - 4x = - 3 + 2 \\ 2x = -1\\ x = \frac{ - 1}{2} \\ x = a1 = \frac{ - 1}{2}$

$a2 - a1 = r \\ 2x + 1 - x = r \\ x + 1 = r \\ \frac{ - 1}{2} + 1 = r \\ \frac{ - 1 + 2}{2} = r \\ r = \frac{1}{2}$

$a100 = a1 + 99r \\ a100 = \frac{ - 1}{2} + 99 \times \frac{1}{2} \\ a100 = \frac{ - 1 + 99}{2} \\ a100 = \frac{98}{2} \\ a100 = 49$