Question 16, Exercise 4.5

Solutions of Question 16 of Exercise 4.5 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

A hot-air balloon rises $80 ft$ in the first minute of flight. If in each succeeding minutes the balloon rises only $90\%$ as far as in the previous minute, what will be its maximum altitude if it is allowed to rise without limit?

Solution. Let balloon raise the hight $a_1$, $a_1 r$, $a_1 r^2$, … in each minute. Then $=a_1= 80 ft$
Ratio of rise in each minute $r=90% = \frac{90}{100} =0.9$.
If $A$ represent maximum altitude of the balloon, then \begin{align} A &= a_1+a_1r+a_1r^2+... \\ & = \frac{a_1}{1-r} \\ & = \frac{80}{1-0.9}\\ &= 800 \end{align} Hence maximum altitude of the baloon will be $800 ft$.

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