Question

Wyznacz wzór ogólny ciągu arytmetycznego. a) a₁ = 6, a3 = 20
b) a₁ = -4, a4 = 5​

Answer 1

Odpowiedź:

a) an = 7n - 1

b) an = 3n - 7

Szczegółowe wyjaśnienie:

a) Skoro a1 = 6 i a3 = 20 to:

a3 = a1 + 2r

20 = 6 + 2r

14 = 2r

r = 7

an = a1 + (n - 1)r = 6 + (n - 1) ▪︎ 7 = 6 + 7n - 7 = 7n - 1

b) Skoro a1 = - 4 i a4 = 5 to:

a4 = a1 + 3r

5 = - 4 + 3r

9 = 3r

r = 3

an = a1 + (n - 1)r = - 4 + (n - 1) ▪︎ 3 = - 4 + 3n - 3 = 3n - 7