Question 30, Exercise 4.4

Solutions of Question 30 of Exercise 4.4 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 5-day rain caused the river to rise. After the first day, the river rose one inch. Each day the rise in the river tripled. How much had the river risen after 5 days?

Solution.

Suppose rise in river:

after 1st day =a1=1 inch
after 2nd day =a2=3 inch
after 3rd day =a3=3×3=9 inch
after 4th day =a4=3×9=27 inch
after 5th day =a5=3×27=81 inch.

Hence the river will rise 81 inch after five days. GOOD

Alternative Method:

Take a1=1 and r=3.

Then rise in river after five day a5=?

From the given data, we have geometric sequence with an=a1rn1. implies a5=a1r4=(1)(3)4=81 Hence river will rise 81 inch after five days. GOOD

If one conclude that the rise in river is with respect to the previous day. Then the total rise in river after five days will be Sn=a1+a2+a3+a4+a5.