Exam-Style Question on Sequences
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 21. This question is similar to one that appeared on an IB Studies paper in 2012. The use of a calculator is allowed.
Chris checks his Twitter account and notices that he received a tweet at 8:00am. At 8:05am he forwards the tweet to four people. Five minutes later, those four people each forward the tweet to four new people. Assume this pattern continues and each time the tweet is sent to people who have not received it before.
The number of new people who receive the tweet forms a geometric sequence:$$1 , 4 , …$$
(a) Write down the next two terms of this geometric sequence.
(b) Write down the common ratio of this geometric sequence.
(c) Calculate the number of people who will receive the tweet at 8:40am.
(d) Calculate the total number of people who will have received the tweet by 8:40am.
(e) Calculate the exact time at which a total of 5 592 405 people will have received the tweet.
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.
Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.
This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.
A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.
Drag this panel down to reveal the solution
If you need more practice try the self-checking interactive exercise called Sequences and Series.
©1997 - 2020 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/