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Sol cycled to raise funds for a charitable organization. On the first day, he cycled 48km for the first 10 days, he cycled 2km less on each subsequent day. Thereafter, he cycled 2km less on each subsequent day.
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3 partsStep-by-step solution
7 stepsHuu hapa ni ufumbuzi wa swali lako:
Part a(i)· 2 steps
Umbali uliosafiriwa siku ya 10.
Kokotoa
Tambua mfululizo wa hesabu.
Kutokana na maelezo, Soi aliendesha baiskeli 40km siku ya kwanza. Kisha, aliendesha 2km pungufu kila siku inayofuata. Hii inaunda mfululizo wa hesabu (arithmetic progression) ambapo:
Neno la kwanza () = 40 km
Tofauti ya kawaida () = -2 km (kwa sababu umbali unapungua)
Fomula ya neno la katika mfululizo wa hesabu ni .Kokotoa umbali uliosafiriwa siku ya 10.
Tumia katika fomula:
Umbali uliosafiriwa siku ya 10 ni .
Part a(ii)
Umbali uliosafiriwa siku ya 16.
Tumia fomula ya neno la katika mfululizo wa hesabu.
Kama ilivyo hapo juu, km na km.
Kokotoa umbali uliosafiriwa siku ya 16.
Tumia katika fomula:
Umbali uliosafiriwa siku ya 16 ni .
Part b
Ikiwa Soi alikusanya Ksh 200 kwa kila Km, kokotoa jumla ya pesa zilizokusanywa.
Tambua idadi kamili ya siku za kuendesha baiskeli.
Soi ataendelea kuendesha baiskeli hadi umbali uwe 0 au chini. Tutapata wakati .
Kwa hivyo, Soi aliendesha baiskeli kwa siku 21.
Kokotoa jumla ya umbali uliosafiriwa kwa siku zote.
Jumla ya mfululizo wa hesabu ni .
Hapa, , , na (umbali siku ya 21).Kokotoa jumla ya pesa zilizokusanywa.
Kiwango cha kukusanya pesa ni Ksh 200 kwa kila Km.
Jumla ya pesa zilizokusanywa ni .
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