Gp Intro Tricks 57E6B4
1. **Problem Statement:** You want a quick introduction and tricks to solve problems on Geometric Progression (GP) for your exam.
2. **Introduction to GP:** A Geometric Progression is a sequence where each term after the first is found by multiplying the previous term by a constant called the common ratio $r$.
3. **General formula:** The $n$th term of a GP is given by $$a_n = a \times r^{n-1}$$ where $a$ is the first term.
4. **Sum of first $n$ terms:** $$S_n = a \frac{r^n - 1}{r - 1}$$ if $r \neq 1$.
5. **Tricks:**
- If $r=1$, all terms are equal to $a$.
- To find the common ratio quickly, divide the second term by the first.
- Use the sum formula directly for quick calculation.
- For MCQs, check if options fit the formula by plugging in values.
- Remember powers of $r$ grow or shrink fast; use this to estimate answers.
6. **Summary:** Know the formulas, identify $a$ and $r$ quickly, and apply the sum formula for fast answers.
Good luck!