6.01 Introduction to sequences
Identify the following sequences as finite or infinite:
What is the third term in the sequence 4, - 5, 6, - 7, 8?
Find the next number in the sequence 16, 36, 64, 100, 144, \ldots
Find the first five terms of the following sequences. Round the terms to four decimal places where necessary.
For the sequence 3, 0.3, 0.03, 0.003, \ldots , write a formula for the nth term of the sequence, u_n, in terms of n.
Christa deposits \$1 into a new bank account while Jenny deposits \$38 into a new bank account. The next day, Christa adds \$2 to the account, and doubles how much she adds each day thereafter. Jenny adds \$5 each day.
Fill in the amount Christa had in the account each day for the first four days.
Fill in the amount Jenny had in the account each day for the first four days.
On which day will they have the same amount of money?
For a photo, the staff at a company have been arranged such that there are 9 people in the front row and each row has 2 more people than in the row in front of it.
Write a formula for u_n in terms of n.
How many people are in the 10th row?
A basketball is dropped onto the ground from a height of 15 metres. On each bounce, the ball reaches a maximum height of 55\% of its previous maximum height.
Write a formula for u_n, for the height reached on the nth bounce in terms of n.
How high does the basketball reach after the 5th bounce? Round your answer to two decimal places.