Question

sa se calculeze primul,ratia si suma primilor 10 termeni a unei progresii aritmetice in care a18=51 si a30=123

Answer 1

a18=a1+17r________________________a18=51=>a1+17r=51=>a1=51-17r______ a30=a1+29r________________________a30=123=>a1+29r=123=>a1=123-29r___ din relatiile:a1=51-17r si a1=123-29r =>. 51-17r=123-29r___29r-17r=123-51 _____12r=72|:12=>r=6_______________a1=51-17r=51-17•6=51-102=-51_______ a1=-51____________________________S10=[2a1+9r]•10/2=[2•(-51)+9•6]•5=(-102 +54)•5=-48•5=-240

Answer 2

Pai daca a18=51 si a30=123 avem:
a18=a1+(18-1)*r;
a30=a1+(30-1)*r;
apoi: a18=a1+17r⇒a1+17*r=51
        a30=a1+29*r⇒a1+29*r=123
apoi faci sistem de ecuatii:
-a1-17*r=-51
a1+29*r=123 , de unde rezulta 12*r=72⇒r=6
apoi inlocuiesti ratia: a1+17*6=51 ⇒a1+102=51 ⇒a1=-51
iar astfel ai aflat si primul termen!
si acum aflii suma :
S10=[( -51+a10)/2]*10
a10=a1+9*r
a10=-51+9*6
a10=3
S10=[(-51+3)/2]*10
S10=[(-48/2)]*10
S10=-24*10
S10=-240
Sper sa fie corect!!!!