Question

Rozwiąż ciąg arytmetyczny. 3 zadanie​

Answer 1

Odpowiedź:

zad 3

a₁ = x+ 8

a₂= 2x+ 3

a₃= 4x- 5

a₃ - a₂ = a₂ - a₁

4x- 5 - 2x - 3 = 2x + 3 - x - 8

2x- 8 = x - 5

2x - x = - 5 + 8

x = 3

a₁ = x + 8 = 3 + 8 = 11

a₂ = 2x+ 3 = 2 * 3 + 3 = 6 + 3 = 9

a₃ = 4x- 5= 4 * 3 - 5 = 12 - 5 = 7

r - różnica ciągu = a₂ - a₁ = 9 - 11 = - 2

an = a₁ + (n - 1) * r = 11 + (n - 1) * ( - 2) = 11 - 2n + 2 = - 2n + 13

a₈ = a₁ + 7r = 11 + 7 * (- 2)= 11 - 14 = - 3

S₈ = (a₁ + a₈) * 8/2 = (11 - 3) * 4 = 8 * 4 = 32