Subjects algebra

Gp Intro Tricks 57E6B4

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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!