# Exam-Style Question on Sequences

## A mathematics exam-style question with a worked solution that can be revealed gradually

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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.

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