Math Problem Statement

1 + 2 + 3 + 4 + 5 + .... + 50 = ?

Solution

The image shows the sum:

1+2+3+4+5++501 + 2 + 3 + 4 + 5 + \dots + 50

This is an arithmetic series, where the first term a=1a = 1, the last term l=50l = 50, and the number of terms n=50n = 50. The formula for the sum SnS_n of an arithmetic series is:

Sn=n2×(a+l)S_n = \frac{n}{2} \times (a + l)

Substituting the known values:

S50=502×(1+50)=25×51=1275S_{50} = \frac{50}{2} \times (1 + 50) = 25 \times 51 = 1275

So, the sum is 1275.

Would you like further details or clarifications?

Here are 5 related questions:

  1. What is the general formula for an arithmetic sequence?
  2. How would the sum change if the sequence ended at 100 instead of 50?
  3. How do you determine the common difference in an arithmetic series?
  4. What is the difference between an arithmetic series and a geometric series?
  5. How would you approach the sum of an infinite arithmetic series?

Tip: For large arithmetic series, knowing the first and last term helps you compute the sum much faster!

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Math Problem Analysis

Mathematical Concepts

Arithmetic Series
Summation

Formulas

Sum of an arithmetic series: S_n = (n/2) * (a + l)

Theorems

Arithmetic series summation

Suitable Grade Level

Grades 6-8