Question

{a_n}=(1,3,6,10,15,....) wyznacz wzor na na n-ty wyraz ciagu

Answer 1

Answer 2

a1 = 1, a2 = 3, a3 = 6, a4 = 10, a5 = 15

a2-a1 = 3-1 = 2

a3-a2 = 6-3 = 3

a4-a3 = 10-6 = 4

a5-a4 = 15-10 = 5

 

Ciąg arytmetyczny tworzą róznice wyrazów tego ciągu:

r = n ∈ N+

 

Sn = (a1+an)*n/2

Sn = an

a1 = 1

an = (1+an)*n/2

an = n

an = (1+n)*n/2 = n/2 + n²/2

an = n²/2 + n/2