Series and Sequences Tutorials
Group Work Assignment
Q1. Jasper is saving for a new car. He puts USD $100 into his savings account and then each month he puts in USD
$10 more than the month before. Jasper needs USD $1200 for the car. Assuming no interest is added, find,
a) The amount Jasper has saved after four months,
b) The month in which Jasper reaches his goal of USD $1200.
Q2. A new virus is circulating on a remote island. On day one there were 10 people infected, with the number of
new infections increasing at a rate of 40% per day.
a) Find the expected number of people newly infected on the 7 th day.
b) Find the expected number of infected people after one week (7 days), assuming no one has recovered yet.
Q3. A factory owner repays his loan of Ksh 2088000 by Ksh 20000 in the first monthly installment and then increases
the payment by Ksh 1000 in every installment. How many installments will it take for him to clear his loan?
Q4. The value of an automobile depreciates at the rate of 15% per year. What will the value of an automobile be
after three years if it is purchased for 4500 dollars?
Q5. James intends to buy a car worth Ksh 2,300,000. He embarks on a savings scheme which follows an Arithmetic
Progression (AP) in which he saves Ksh. 150,000 in the first month and increases her subsequent savings by Ksh
20,000 each month. Determine the amount he will require to borrow to achieve his dream by the time he has saved
for 8 months.
Q6. An investor bought a piece of land for Ksshs. 2,500,000 in January 2018 in Nairobi west. The value of land
appreciated by 18% per annum in the year 2018 and 2019. The land further appreciated by 15% per annum in 2020.
Due to the harsh economic conditions caused by the effects of corona the value of land depreciated by 12% during
the year ending 2021.
a) The expected value of Land by the end of year 2021
b) The rate of interest per annum that could have resulted in the land appreciating to the same value after
four years
Q7. John bought a personal car for Ksh. 2,800,000 at the start of January 2021. The value of the car depreciates at
1% per month. Determine the expected value of the car as at 31st December 2022.
Q8. John bought a house at the start of year 2012 for Ksh. 40 million. The value of the house has been appreciating
at a rate of 4% per annum. Determine the value of the house at the end of year 2027.
Q9. The ninth, thirteenth and fifteenth terms of an arithmetic progression are the first three terms of a geometric
progression whose sum of infinity is 80. The sixteenth term of an arithmetic progression is equal to the fourth term
of the geometric progression. Calculate the sum of the first sixteen terms of the arithmetic progression.
Q10. If the first, third and thirteenth terms of an arithmetic progression are in geometric progression, and the sum
of the fourth and seventh terms of this arithmetic progression is 40, find the first term and the (non-zero) common
difference.