👤
a fost răspuns

bunaaaaaaa. cine se pricepe la matematica? :3 :D :)

Fie (an) o progresie aritmetica si Sn suma primilor n termeni. Sa se calculeze:
a) 3 S100- 3S200 +S300
b) 3 ( Sn- S2n ) + S3n

Răspuns :

Stef90
Sn=a1*n+r*n*(n-1)/2
a)
3(100a1+50*99r)-3(200a1+100*199r)+300a1+150*299r=
150*99r-300*199r+150*299r=
150r(99-398+299)=0
b)3(a1*n+r*n*(n-1)/2 - a1*2n + r*2n(2n-1)/2+a1*3n+r*3n(3n-1)/2=
a1(3n-6n+3n) + r*[3*n(n-1)/2 - 3n(2n-1) + 3n(3n-1)/2 ]= 0



Alte intrebari