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What is the 8th term of the sequence below?2240, 1120, 560, 280, ..8.25

Sagot :

Given a sequence as shown below

[tex]2240,\text{ 1120 , 560 , 280, }\ldots\ldots\ldots\ldots.\text{ 8.75}[/tex][tex]\begin{gathered} Firstterm(T_1)\text{= 2240} \\ Secondterm(T_2)\text{= 1120} \\ Thirdterm(T_3)\text{= 560} \end{gathered}[/tex]

From the observation

[tex]\frac{T_2}{T_1}\text{ =}\frac{T_3}{T_2}=\text{ }\frac{1120}{2240}\text{ =}\frac{560}{1120}\text{ = }\frac{1\text{ }}{2}[/tex]

For the 8th term

[tex]\begin{gathered} 2240\text{ x (}\frac{1}{2})^{8-1} \\ 2240\text{ x (}\frac{1}{2})^7 \\ 2240\text{ x }\frac{1}{128} \\ 17.5 \end{gathered}[/tex]

Hence the 8th term of the sequence = 17.5

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