Math Problem Statement
What is the sum of all even numbers between 1 and 51? indicate and demonstrate simple step by step formula.
Solution
To find the sum of all even numbers between 1 and 51, we can use a simple mathematical formula for the sum of an arithmetic sequence.
Step-by-Step Solution:
-
Identify the even numbers between 1 and 51: The even numbers between 1 and 51 are: 2, 4, 6, ..., 50.
-
Identify the first term (a) and the last term (l) of the sequence:
- First even number
- Last even number
-
Find the number of terms (n): The difference between consecutive even numbers is 2, and the sequence starts at 2 and ends at 50.
To find the number of terms in the sequence, use the formula: Substituting values: So, there are 25 even numbers between 1 and 51.
-
Use the formula for the sum of an arithmetic sequence: The sum of the first terms of an arithmetic sequence is given by: Substituting values:
Thus, the sum of all even numbers between 1 and 51 is 650.
Do you want any further details or have questions?
Related questions:
- How would the formula change if you sum odd numbers instead of even numbers?
- How do you find the sum of even numbers between any two given numbers?
- What is the sum of all odd numbers between 1 and 51?
- Can you find the sum of all multiples of 3 between 1 and 100?
- How does the arithmetic sequence formula work for a geometric progression?
Tip:
When summing numbers that follow a regular pattern (like even numbers), the arithmetic sequence formula can greatly simplify your calculations.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Summation of Series
Formulas
Sum of an arithmetic sequence: S_n = (n/2) * (a + l)
Formula for number of terms in an arithmetic sequence: n = (l - a)/d + 1
Theorems
Arithmetic Sequence Sum Formula
Suitable Grade Level
Grades 6-8