# CONVERTING RECURSIVE AND EXPLICIT FORMULA OF THE SEQUENCE WORKSHEET

Problem 1 :

You have read 25 pages of a book. You plan to read an additional 10 pages each night. Write the explicit formula to represent the number of pages you will read after n nights.

Solution

Problem 2 :

In 2014, the cost to mail a letter was 49 cent for up to one ounce. Every additional ounce costs 21 cent. Which recursive function could be used to determine the cost of 3 ounce letter in cents.

(a)  a1 = 49, an = an-1 + 21

(b)  a1 = 21, an = an-1 + 49

(c)  a1 = 0, an = 49an-1 + 21

(d) a1 = 0, an = 21an-1 + 49

Solution

Problem 3 :

A bicyclist is training for a race. On the first day of training, she rides 12 miles. She increases the distance she rides by 3 miles each day. Write an explicit formula to represent this scenario. How many miles will the bicyclist ride on her ninth day of training ?

Solution

Problem 4 :

Sofie needs to complete community service hours for her service club. She needs to complete 150 hours to earn a merit badge. Sofie has already completed 65 hours.

Write an explicit formula to represent this scenario. If she volunteers 5 hours each week, in how many weeks will she have completed the hours to earn the merit badge ?

Solution

Problem 5 :

The first term of a sequence equals 5. Each term in the sequence can be obtained by subtracting 3 from twice the value of the prior term.

a) List the first four terms of the sequence.

b) Write the recursive formula for the sequence.

c) Is this an arithmetic sequence ? Explain

Solution

Problem 6 :

The graph of an arithmetic sequence is shown to the right.

a) List the first four terms of the sequence.

b) Write the recursive formula for the sequence.

c) Find an explicit formula for the sequence.

Solution

1)  25 + 10n

2)  a2 = 70, a3 = 91

3)  36 miles

4)  17 weeks

5)   a)  5, 7, 11, 19    b)  After 17 hours.

6)  a)  -2, 1, 4, 7, ....

b)  an = an-1 + 3

c)   -5 + 3n

Solution

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