# Section 2 Quiz #2 Key

```Quiz #2
Sequences and Series
Name:
KEY
Show enough work that I can reproduce your results.
No Calculators. You may leave answers in unsimplified form.
1.
Write each series in  notation:
23
 91   (1  4k )
a. 3  7  11  15 
k 1
(1) k  (3k  2)
5k 1
k 1

8 11 14 17
b. 5  



5 25 125 625
2 5
7k
k 1

2.
Evaluate the infinite sum:
3.
Evaluate the sum:

99
k 3
 
k  k 1 
 
4 5 


k
k 1
 
5 6 


k
k 1
2
5
 k
k
k 1 7
k 1 7


6 7 


2
25
2 25
121
 7  7  

2
5 5 2
10
1
1
7
7

99  100  4  100  8
4.
The steps on most ladders are narrower at the top than at the bottom. Assume that their lengths
form an arithmetic sequence. Given that the top step is 18 inches and the bottom step is 24
inches and there are 13 steps,
a.
what is the sum of the lengths of all the steps?
d
24  18 6

 .5
13  1 12
So, Sum of lengths = 18  18.5  19 
b.
 24 
12
(18  24)  240 inches
2
what is the length of the 4th step from the bottom ? 18  .5(4)  20 inches
5. Evaluate the sum: 3  1  5  9  13 
 441
This is an arithmetic series with an  3  4(n  1)  4n  7 .
Setting 441  4n  7  4n  448  n  112 .
112
 441 
(3  441)  56  438  24,528
So, 3  1  5  9  13 
2
```