Mehlala ea Lipotso tse Buisanang ka Tatellano ea Lipalo
Tatellano ea lipalo ke khopolo ea motheo lipalong tse hlahang khafetsa litlhahlobong tse fapaneng le lits'ebetsong tsa lefats'e la nnete. Tatellano ea lipalo ke tatellano ea linomoro e nang le phapang e sa fetoheng lipakeng tsa mantsoe a mabeli a latellanang. Sehloohong sena, re tla hlahloba khopolo ea tatellano ea lipalo ka botebo ka mathata a 'maloa a mehlala a tsamaeang le litlhaloso tse felletseng.
Litlhaloso le Litlhaloso
Pele re kena mathateng a mohlala, ho bohlokoa ho utloisisa mongolo o atisang ho sebelisoa tatellanong ea lipalo. Haeba \(a\) e le lentsoe la pele 'me \(d\) e le phapang e tloaelehileng (phapang e sa fetoheng), joale tatellano ea lipalo e ka ngoloa ka tsela ena:
\[ a, a+d, a+2d, a+3d, \ldots, a+(n-1)d \]
Lentswe la bohlano (Un) la tatellano ena le ka hlophiswa ka tsela ena:
\[ U_n = a + (n-1)d \]
Tse latelang ke mehlala e 'maloa ea lipotso le lipuisano tsa tsona ho etsa hore ho be bonolo ho utloisisa tatellano ea lipalo.
Mohlala oa Potso ea 1
Potso:
Ha ho fanoe ka tatellano ea lipalo ka lentsoe la pele \(a = 5\) le phapang e tloaelehileng \(d = 3\). Fumana lentsoe la bo10 la tatellano.
Puisano:
Ho sebelisoa foromo e akaretsang bakeng sa lentsoe la nth, e leng \( U_n = a + (n-1)d \):
\[ U_{10} = 5 + (10-1) \cdot 3 \]
\[ U_{10} = 5 + 9 \cdot 3 \]
\[ U_{10} = 5 + 27 \]
\[ U_{10} = 32 \]
Kahoo, nako ea bo10 ea tatellano ke 32.
Mohlala oa Potso ea 2
Potso:
Ha ho fanoe ka tatellano ea lipalo moo nako ea bohlano e leng 20 'me nako ea borobeli e le 35. Fumana nako ea pele \(a\) le phapang e tloaelehileng \(d\) ea tatellano.
Puisano:
Ho tsoa potsong, rea tseba:
\[ U_5 = a + 4d = 20 \]
\[ U_8 = a + 7d = 35 \]
Tlosa di-equation ka bobedi ho tlosa \(a\):
\[ (a + 7d) – (a + 4d) = 35 – 20 \]
\[3d = 15 \]
\[d = 5 \]
Jwale re nkela sebaka sa \(d = 5\) ho fumana \(a\):
\[ a + 4 \cdot 5 = 20 \]
\[a + 20 = 20 \]
\[a = 0 \]
Kahoo, lentsoe la pele la tatellano ke 0 mme phapang ke 5.
Mohlala oa Potso ea 3
Potso:
Kakaretso ea mantsoe a pele a 20 a tatellano ea lipalo eo lentsoe la eona la pele e leng \(a = 2\) le phapang e tloaelehileng \(d = 4\) ke bokae?
Puisano:
Kakaretso ea mantsoe a pele a n a tatellano ea lipalo e ka baloa ho sebelisoa foromo:
\[ S_n = \frac{n}{2} \left( 2a + (n-1)d \right) \]
Bakeng sa mola ona:
\[ S_{20} = \frac{20}{2} \left( 2 \cdot 2 + (20-1) \cdot 4 \right) \]
\[ S_{20} = 10 \ka ho le letshehadi( 4 + 76 \ka ho le letona) \]
\[ S_{20} = 10 \cdot 80 \]
\[ S_{20} = 800 \]
Kahoo, kakaretso ea mantsoe a 20 a pele a tatellano ke 800.
Mohlala oa Potso ea 4
Potso:
Tekanyo ea boraro ea tatellano ea lipalo ke 15 'me tekanyo ea bosupa ke 27. Fumana tekanyo ea bo12 ea tatellano.
Puisano:
Taba ea pele, re hloka ho fumana boleng \(a\) le \(d\). Ho tsoa potsong, rea tseba:
\[ U_3 = a + 2d = 15 \]
\[ U_7 = a + 6d = 27 \]
Tlosa di-equation ka bobedi ho tlosa \(a\):
\[ (a + 6d) – (a + 2d) = 27 – 15 \]
\[4d = 12 \]
\[d = 3 \]
Jwale re nkela sebaka sa \(d = 3\) ho fumana \(a\):
\[ a + 2 \cdot 3 = 15 \]
\[a + 6 = 15 \]
\[a = 9 \]
Ho sebedisa foromo ya nth term ho fumana term ya bo12:
\[ U_{12} = a + 11d \]
\[ U_{12} = 9 + 11 \cdot 3 \]
\[ U_{12} = 9 + 33 \]
\[ U_{12} = 42 \]
Kahoo, nako ea bo12 ea tatellano ke 42.
Mohlala oa Potso ea 5
Potso:
Tatellano ea lipalo e nang le lentsoe la pele \(a\) le phapang e tloaelehileng \(d\) e na le kakaretso ea mantsoe a pele a 10, e leng 55. Haeba \(d = 1\), fumana lentsoe la pele \(a\).
Puisano:
Fanoeng \(d = 1\) le \(S_{10} = 55\). Sebedisa foromo bakeng sa kakaretso ya mantswe a pele:
\[ S_n = \frac{n}{2} (2a + (n-1)d) \]
Bakeng sa n = 10:
\[ S_{10} = \frac{10}{2} (2a + 9 \cdot 1) = 55 \]
\[ 5 (2a + 9) = 55 \]
\[ 2a + 9 = 11 \]
\[ 2a = 2 \]
\[a = 1 \]
Kahoo, lentsoe la pele la tatellano ke 1.
Qetello
Tatellano ea lipalo ke khopolo ea motheo lipalong tse thusang haholo masimong a fapaneng. Sehloohong sena, re buisane ka mehlala e 'maloa ea tatellano ea lipalo le litharollo tsa tsona. Kutloisiso e ntle ea liforomo le litšobotsi tsa motheo tsa tatellano ea lipalo e tla thusa haholo ho rarolla mefuta e fapaneng ea mathata a amanang le sehlooho sena.
Ka ho itloaetsa mehlala e kang e ka holimo, ho tšeptjoa hore u tla ba le tsebo e kholoanyane le ho potlakela ho rarolla mathata a amanang le tatellano ea lipalo.
