This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Step 1: Tambua mpangilio wa namba zilizopewa. Angalia namba tatu za kwanza: Namba hizi ni miraba kamili.
Step 2: Tambua mpangilio wa namba za msingi. Namba za msingi ni . Tunaona kwamba kila namba inayofuata inapungua kwa .
Step 3: Tafuta namba ya msingi inayofuata. Kufuatia mpangilio, namba ya msingi inayofuata baada ya itakuwa .
Step 4: Tafuta namba inayofuata katika mfuatano. Namba inayofuata katika mfuatano itakuwa mraba wa namba ya msingi tuliyoipata:
Step 5: Linganisha namba inayofuata na na utafute thamani ya . Tunajua kwamba namba inayofuata ni , na katika mfuatano imeandikwa kama . Hivyo, tunaweza kuweka sawa: Ili kupata , gawanya pande zote mbili kwa :
Thamani ya ni .
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Tambua mpangilio wa namba zilizopewa. Angalia namba tatu za kwanza: 144 = 12^2 100 = 10^2 64 = 8^2 Namba hizi ni miraba kamili.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.