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About Pawan Musale
Expertise
I can answer Basic Mathematics questions like: Natural Numbers, Integers, Real Numbers, Complex Numbers, Number Theory, Geometry, Trigonometry, Graph Theory, Square Roots, Basic Integration, Profit-Loss problems, Work-Time problems, Equations etc I can try to answer questions of probability and set theory

Experience
I am tutoring school children (10-15 years age group) since last 5 years.

Education/Credentials
I am Bachelor in Engineering (Instrumentation) from the reputed institute in India.

Awards and Honors
I was 18th in High School Scholarship examination in Maharashtra State of India. I was second in Mathematics in Maharashtra State in Secondary School Certificate examination.

You are here: Experts > Science > Math for Kids > Basic Math > Algebra Equation

Basic Math - Algebra Equation

Expert: Pawan Musale - 9/24/2009

Question
How many lines does it take to connect 5 employees?
Answer: (5-1)+(5-2)+(5-3)+(5-4)+(5-5)= 10

Find the expression for the number of lines for n employees.

I know this has a simpler equation but I can't figure it out. Help please!

Answer
Bryan,

For 5 employees your equation is:

(5-1)+(5-2)+(5-3)+(5-4)+(5-5)= 10

We will re-write this and will denote as S:

S = 4 + 3 + 2 + 1 + 0

Now let number of employees = n
S = total number of lines

If you observe, in above equation difference between each term is 1. It starts from 0 and ends to 4 with difference of 1 between each term.

So difference = d = 1

Since consecutive terms have constant difference (=1), this is an example of arithmetic progression (AP).

For AP, Sum of all terms is given by equation,

S = n[2*a1+(n-1)*d]/2 ----------------------- #1

S = sum of all terms.
n = total number of terms, here total employees
a1 = first term = 0
d = difference between two consecutive terms = 1

Putting these values in #1 above,

S = n[2*0 + (n-1)*1]/2
S = n(n-1)/2 ------------------------------ #2

So this is the expression for number of lines for n employees.

We can verify it by putting n=5.

So S = 5(5-1)/2 = 20/2 = 10
So #2 is the correct expression.

I believe this helps.

Kindly let me know if you need additional information.

Regards,
Pawan

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