Last Term Of Geometric Progression Calculator

Geometric Progression Formula:

\[ l = a \times r^{(n_{total}-1)} \]

Last Term of Progression (l):

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1. What is the Geometric Progression Formula?

The geometric progression formula calculates the last term of a geometric sequence. A geometric progression is a sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

2. How Does the Calculator Work?

The calculator uses the geometric progression formula:

\[ l = a \times r^{(n_{total}-1)} \]

Where:

\( l \) — Last term of progression
\( a \) — First term of progression
\( r \) — Common ratio of progression
\( n_{total} \) — Number of total terms of progression

Explanation: The formula calculates the nth term of a geometric sequence by multiplying the first term by the common ratio raised to the power of (n-1).

3. Importance of Geometric Progression Calculation

Details: Geometric progressions are fundamental in mathematics and have applications in various fields including finance (compound interest), physics (exponential decay), computer science (algorithm analysis), and population growth models.

4. Using the Calculator

Tips: Enter the first term, common ratio, and total number of terms. All values must be valid numbers. The common ratio cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a geometric progression?
A: A geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Q2: Can the common ratio be negative?
A: Yes, the common ratio can be negative, which results in an alternating sequence where terms switch between positive and negative values.

Q3: What happens if the common ratio is 1?
A: If the common ratio is 1, all terms in the sequence will be equal to the first term, creating a constant sequence.

Q4: Can the common ratio be between 0 and 1?
A: Yes, if the common ratio is between 0 and 1, the sequence will decrease exponentially toward zero.

Q5: What are some real-world applications of geometric progressions?
A: Geometric progressions are used in compound interest calculations, radioactive decay, population growth models, computer algorithms, and many other exponential growth or decay scenarios.