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 80ft 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 a1, a1r, a1r2, … in each minute. Then =a1=80ft
Ratio of rise in each minute r=90.
If A represent maximum altitude of the balloon, then A=a1+a1r+a1r2+...=a11r=8010.9=800 Hence maximum altitude of the baloon will be 800ft. GOOD