Question

calculati suma primilor 20 de termeni ai progresiei aritmetice (an)n>=1, daca : a4-a2=4 si a1+a3+a5+a6=30

Answer 1

an=a1+(n-1)r
a2=a1+r
a3=a1+2r
a4=a1+3r
a5=a1+4r
a6=a1+5r

a4-a2=4
(a1+3r)-(a1+r)=4
a1-a1+3r-r=4
0+2r=4
2r=4 =>r=2

a1+a3+a5+a6=30
a1+(a1+2r)+(a1+4r)+(a1+5r)=30
4a1+11r=30
4a1+11*2=30
4a1+22=30
4a1=30-22
4a1=8 =>a1=2

a20=a1+19r
a20=2+19*2=2+38=40

$\frac{(a1 + a20) \times 20}{2}$
$\frac{(2 + 40) \times 20}{2}$
S20=420