Question

Sa se calculeze suma primilor 5 termeni ai unei progresii aritmeticee $(a _{n} )_{n \geq 1}$ stiind ca a1=-1 si a3=5

Answer 1

an=a1+(n-1)r     n=rangul   r  =ratia
a3=a1+(3-1)R
5=-1+2r  2r=6   r=6/2=3
Ratia r=3
Scrii   formula   sumei unei progresii
SN=(a1+an)*n/2
S5=(-1+a5)*5/2
a5=a1+4r
a5=-1+4*3=11
S5=(-1+11)*5/2=10*5/2=25

Answer 2

Progresie aritmetica.
r-ratia, n-numarul termenilor
a1= -1
a3=5
a3=a1+2r
=> a1+2r=5
-1+2r=5
2r=1+5=6 => r=6:2=3
Sn=suma
Sn=(a1+an)*n/2
In cazul nostru S5
n=5
a5=a1+4r= -1+4×3= 12-1=11
S5=(a1+a5)*n/2
S5=(-1+11)*5/2=10*5/2
S5=50/2=25