Question

Fie progresia aritmetica (an) n>1 . Calculati a1 si n daca se cunosc an=17 Sn =56 si r=3.

Answer 1

an=17 ; Sn =56 si r=3

an=a1+(n-1)r

a1=an-(n-1)r=an-nr+r

Sn=(a1+an)•n/2

Sn=(an-nr+r+an)•n/2

2Sn=(2an-nr+r)•n

2•56=(34-3n+3)•n

112=37n-3n²

3n²-37n+112=0

Δ=1369-1344=25

n1=(37+5)/6=42/6=7

n2=(37-5)/6 =32/6, nu convine

n=7

a1=an-(n-1)r=17-6•3=-1

R :a1=-1 si n=7