Question

rozwiąż równanie (ciągi):
2 + 5 + 8 + ... + x = 155

Answer 1

Odpowiedź:

Szczegółowe wyjaśnienie:

a₁ = 2 , r = 3 , an = x   , Sn = 155   gdzie n ∈ N+

x = an = a₁ + r(n - 1) = 2 + 3(n - 1) = 2 + 3n - 3 = 3n - 1

Sn = 1/2 * (a₁ + an) * n = 1/2 * (2 + 3n - 1) * n = 1/2 * (3n + 1) * n = (3/2) n² + (1/2) n = 155              

(3/2) n² + (1/2) n - 155 = 0         I * 2

3n² + n - 310 = 0

3n² - 30n + 31n - 310 = 0

3n(n - 10) + 31(n - 10) = 0

(3n + 31)(n - 10) = 0

3n + 31 = 0  I - 31

3n = -31     I : 3

n = -31/3 = -10 i 1/3  

-10 1/3 ∉ N+

lub

n - 10 = 0         I + 10

n = 10  , 10 ∈ N+

x = a₁₀ = 3 * 10 - 1 = 30 - 1 = 29