How to Solve Problems in Arithmetic Series Using Formulas?

In summary, the conversation is about understanding how to apply the formulas for arithmetic means and series to specific problems. The speaker is struggling with finding the answer for two different problems involving arithmetic series and is seeking help. The formula for arithmetic series is Sn=n/2 (A1+An), which can also be written as Sn=n/2 [2A1+(n-1)d].
  • #1
bananaman13
2
0
I don't understand on how to get the answer of a certain problem in arithmetic series.

formula/s:

Arithmetic means

An=A1+ (n-1)d

Arithmetic series

Sn=n/2 (A1+An)

I understand on how to get the terms to these but when finding for:

Find A1 if,
S10= -20 , d= 4

&

Find S12 if, 2+5+8+...

I couldn't quite grasp the idea on how to apply the formulas to these problems.

Any help is appreciated. Thank you very much
 
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  • #2
Sn=n/2 (A1+An)

this can also be written as Sn=n/2 (A1+(A1+ (n-1)d))

which then further simplifies to: Sn=n/2 (2A1+ (n-1)d)

now plug in the known values and simplify

for your first question, the value of n=10

for your second question,
n=12,d=3,A1=2
 
  • #3
Thank you so much.

So, in which case,

Sn=n/2 (A1+An) is still equal to
Sn=n/2 [2A1+(n-1)d]

Just different in how to solve it.
 

Related to How to Solve Problems in Arithmetic Series Using Formulas?

1. What is an arithmetic mean?

The arithmetic mean is a mathematical term that refers to the average of a set of numbers. It is found by adding all the numbers in the set and dividing the sum by the total number of values in the set.

2. How is the arithmetic mean calculated?

The arithmetic mean is calculated by adding all the numbers in the set and then dividing the sum by the total number of values in the set. The formula for calculating the arithmetic mean is: mean = (sum of all values) / (total number of values).

3. What is the difference between arithmetic mean and geometric mean?

The arithmetic mean is the sum of a set of numbers divided by the number of values in the set, while the geometric mean is the nth root of the product of a set of numbers. The arithmetic mean is used to find the average, while the geometric mean is used to find the central tendency of a set of numbers.

4. What are arithmetic series and how are they used?

An arithmetic series is a sequence of numbers where the difference between consecutive terms is constant. It is used to find the sum of a sequence of numbers or to determine the missing term in a sequence. The formula for calculating the sum of an arithmetic series is: Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference.

5. How are arithmetic means and series used in real life?

Arithmetic means and series are used in various real-life situations, such as calculating the average test scores of a class, determining the average monthly income of a household, or finding the total cost of a trip with changing expenses. They can also be used in financial planning, budgeting, and investment analysis.

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