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Answer Key & Solutions to Quiz #1 Finding the Sum of Series
  Posted: May 7th, 2015

Quiz #1 Finding the Sum of a Series

Answer Key to Quiz #1
Problems
Answer
1.
a
2.
b
3.
b
4.
c
b
6.
c
7.
a
 
Solution to Problem #3
Find the sum of the series.
 
Use Property 4 to separate the sequence into 2 groups.
sum in two groups
 
Use Property 2 to put the constant 3 in the second term in front of the sigma notation.
Sigma notation in two groups.
 
use Summation Rule 2
Rule 2 used on sum for question 3.
 
Sum rule 2 used for first term.
 
Simplify first term with sum rule 2.
 
Simplified first term of sequence in sigma notation.
 
- use Summation Rule 1 for i in the second term of the expression.
Summation rule 1 for i in second term plugged in.
 
Reduced terms of sum 1.
Solution to the sum of the series between 1 and 54.

49,500 is not the answer because we are looking for the sum of the series between 25 and 54 not 1 and 54.

Must find the sum of the series between 1 and 24 and subtract that number from the sum of the series between 1 and 54 which is 49,500.
Find the sum of the series between 1 and 24 of the sequence.
Series of the sequence between 1 and 24 being simplified by the summation rules.
Sum of sequence between 1 and 24 being plugged in and solved for.
Sum of series between 1 and 24 being simplified and reduced further.
 
Sum between 1 and 24 fully reduced to numbers, a subtraction problem.
Solution to sum of series between 1 and 24 is 4,000.
Subtract 4,000 from 49,500 to find the sum of the series for
Original problem we are trying to solve, the sum of the series between 25 and 54 for a sequence.
The sum of the series is 45,500.
 

 

Solution to Problem #5
 
Sigma notation problem #5 find the sum of the series.
 
Using summation property 3 to solve problem #5 on math quiz 1.
 
Step 3 to solving problem 5.
 
Step 4 problem 5.
 
Step 5 problem 5.
 
Solution to problem 5.
The sum of the series is 21,285.
 

 

 
 
 
 
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

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