Shortcut Methods

Shortcuts and Tricks for JEE/CBSE Numericals

Arithmetic Progressions (AP)

If $a$ and $b$ are the first and last terms, and $n$ the number of terms in an AP, then the sum of the terms, $S_{n}$ , is given by: $S_{n} = \frac{n}{2} (a + b)$
The $n$ -th term, $T_{n}$ , of an AP with first term $a$ and common difference $d$ is given by: $T_{n} = a + (n - 1) d$

Geometric Progressions (GP)

The sum of the first $n$ terms of a GP with first term $a$ and common ratio $r$ is given by: $S_{n} = \frac{a (1 - r^{n})}{1 - r}, r \neq 1$
The $n$ -th term, $T_{n}$ , of a GP with first term $a$ and common ratio $r$ is given by: $T_{n} = a r^{n - 1}$

Harmonic Progressions (HP)

The sum of the first $n$ terms of a HP with first term $a$ and common difference $d$ is given by: $S_{n} = \frac{n}{2 a} [1 + (n - 1) d]$
The $n$ -th term, $T_{n}$ , of a HP with first term $a$ and common difference $d$ is given by: $T_{n} = \frac{a}{n}$

Shortcut Methods

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Shortcut Methods

Shortcuts and Tricks for JEE/CBSE Numericals

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