Suma de N términos consecutivos en una progresión Geométrica

How to Sum Consecutive Terms in a Geometric Progression

Understanding the Basics of Summing Terms

• The process of summing n consecutive terms in a geometric progression requires knowledge of the first term, the common ratio, and the number of terms to sum.

• The common ratio can be determined by dividing one term by its preceding term; for example, dividing 6 by 3 gives a ratio of 2.

Applying the Formula for Summation

• In this example, the first term is identified as 3 (the initial value), and 'n' is set to 5 (the number of terms to sum).

• The formula used for summation incorporates these values: S_n = a_1 times r^(n - 1) div (r - 1) , where S_n represents the sum.

Step-by-Step Calculation

• Calculating r^n : Here, r^5 = 2^5 = 32 . Then subtracting r - 1: which results in 2 - 1 = 1 .

• Continuing with calculations: After substituting into the formula, we find that multiplying gives us S_n = a_1 times (32 - 1)/1 = 3 times 31.

Final Result Interpretation

• The final result indicates that the sum of these specific consecutive terms equals 93. This method allows for quick calculation without manually adding each term.