For the following geometric sequence, find the recursive formula.
[-80, 20, -5,

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Ответ:

zarakanchi

02.04.2022

Mathematics

Let from the height at which ball was thrown = h units

It is given that , ball rebounds the same percentage on each bounce.

Let it rebounds by k % after each bounce.

Height that ball attains after thrown from height h(on 1 st bounce)= $h + \frac{h k}{100}=h \times (1+\frac{k}{100})$

Height that ball attains after thrown from height h (on 2 n d bounce)= $h \times (1+\frac{k}{100})+h \times (1+\frac{k}{100})\times \frac{k}{100}=h \times (1+\frac{k}{100})^2$

Similarly, the pattern will form geometric sequence.

S= $h +h \times (1+\frac{k}{100})+h \times (1+\frac{k}{100})^2+h \times (1+\frac{k}{100})^3+.........$

So, Common Ratio = $\frac{\text{2nd term}}{\text{1 st term}}=1 +\frac{k}{100}$

Common Ratio= 1 + the percentage by which ball rebounds after each bounce

the percentage by which ball rebounds after each bounce= negative integer= k is negative integer.

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For the following geometric sequence, find the recursive formula. [-80, 20, -5,