Salut!
Care este formula termenului general?
Formula termenului general este: [tex]a_{n} =a_{1} +(n-1)*r[/tex]
a) [tex]a_{1} =-4[/tex] , [tex]r_{} =\frac{1}{7}[/tex] , [tex]a_{15} =?[/tex]
Daca stim ratia si primul termen putem folosi:
[tex]a_{15} =a_{1} +14*r[/tex]
[tex]a_{15} =-4+\frac{1}{7} =\frac{-28+1}{7} =-\frac{27}{7}[/tex]
b)[tex]a_{4} =18[/tex] , [tex]a_{6} =26[/tex] , [tex]a_{1} =?[/tex] , [tex]r_{} =?[/tex]
In acest caz putem face sistem:
[tex]a_{4} =a_{1} +3*r=18[/tex]
[tex]a_{6} =a_{1} +6*r=26[/tex]
------------------------------(-)
/ - 3*r=-8=>-r=[tex]-\frac{3}{8}[/tex] | *(-1)
[tex]r_{}=\frac{3}{8}[/tex]
[tex]a_{1} +3*r=18=>a_{1} =18+\frac{9}{8} =\frac{153}{8}[/tex]
c)[tex]a_{2}=5 ,r=3,a_{8} =?[/tex]
[tex]a_{2} =a_{1} +r=>a_{1} =a_{2} -r=5-3=2[/tex]
[tex]a_{8} =a_{1} +7*r=2+21=23[/tex]
d)[tex]a_{1} =7 ,a_{7} =37,s_{10} =?[/tex]
Formula pentru suma este:[tex]S_{n} =\frac{(a_{1} +a_{n})*n }{2}[/tex]
[tex]a_{7} =a_{1} +6*r=>r=5[/tex]
[tex]S_{10} =\frac{(a_{1}+a_{10})*10 }{2} =295[/tex]
e)[tex]a_{3} +a_{6} +a_{8} =22,S_{5} =10[/tex]
[tex]3*a_{1} +14*r=22|:3\\a_{1} +4*r=\frac{22}{3} =>a_{5} =\frac{22}{3} \\S_{5} =\frac{(a_{1}+a_{5} )*5 }{2}[/tex]
Sper ca te-am ajutat!
