Question

Dacă se cunosc doi termeni ai unei progresii aritmetice (cn) c3=7 si c5=13 sa se găsească c9,C2,c15

Answer 1

cn=c1+(n-1)r
c3=c1+2r=7 
c5=c1+4r=13
inmultim prima relatie cu -2
-2c1-4r=-14
   c1+4r=13
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-c1         =-1, c1=1
2r=7-c1=7-1=6, r=3
c9=c1+(9-1)r
c9=1+24=25
c2=c3-r=4
c15=c1+(15-1)r=1+14x3=43

Answer 2

$c_5=c_3+2r \\\\ 13=7+2r \ \ \ |(-7) \\\\ 6=2r \ \ \ |:2 \\\\ \underline{r=3} \\\\ c_9=c_5+4r \\\\ c_9=13+4*3 \to 13+12=25 \\\\\\ c_2=c_3-r \\\\ c_2=7-3\to 4 \\\\\\ c_{15}=c_5+10r \\\\ c_{15}=13+10*3 \to 13+30=43$