Se considera sirul: 2,9,16,23...
Calculati suma termenilor din sir care sunt mai mari decat 100 si mai mici decat 300.
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2,9,16,23............
a₁=2+7*0=2
a₂=2+7*1=9
a₃=2+7*2=16
a₄=2+7*3=23
2+7*x >100
7x >100-2
7x >98
x >14
a₁= 2+7*15=2+105=107
2+7*x < 200
7*x <200-2
7x <198
x < 28,285..
an= 2+7*28=2+196=198
obtinem:
107+114+121+128......+198
S= (198+107)*(28-14)/2= 305*14/2= 2135
sau :
107+114+121+128......+198= 15*7+2+16*7+2+17*7+2.....+28*7+2=
=7*(15+16+17+...+28)+2*14=7*(15+28)*14/2+2*14=7*301+28=2107+28=
=2135
a₁=2+7*0=2
a₂=2+7*1=9
a₃=2+7*2=16
a₄=2+7*3=23
2+7*x >100
7x >100-2
7x >98
x >14
a₁= 2+7*15=2+105=107
2+7*x < 200
7*x <200-2
7x <198
x < 28,285..
an= 2+7*28=2+196=198
obtinem:
107+114+121+128......+198
S= (198+107)*(28-14)/2= 305*14/2= 2135
sau :
107+114+121+128......+198= 15*7+2+16*7+2+17*7+2.....+28*7+2=
=7*(15+16+17+...+28)+2*14=7*(15+28)*14/2+2*14=7*301+28=2107+28=
=2135
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