Sequences and Series Shortcut - Divide and Rule

Vocabulary flashcards summarizing key concepts, definitions, and specific worked examples for the 'Divide and Rule' shortcut method in sequences and series.

Divide and Rule Shortcut

A mathematical shortcut method used to quickly count how many numbers in a given range are divisible by a specific divisor without constructing an Arithmetic Progression (AP).

Quotient (Divide and Rule)

The integer result obtained after dividing a range limit by the specified divisor, ignoring any remainder.

Absolute Value (Mod) Difference

The step in the shortcut where the quotient of the lower bound is subtracted from the quotient of the upper bound, taking the absolute value to get the final answer.

Two-digit Numbers Range

The range of numbers varying from $10$ to $99$.

Four-digit Numbers Range

The range of numbers varying from $1000$ to $9999$.

Two-digit Numbers Divisible by $4$

Calculated by dividing $10$ by $4$ (quotient $2$) and $99$ by $4$ (quotient $24$), giving an absolute difference of $|2 - 24| = 22$.

Four-digit Numbers Divisible by $7$

Calculated by dividing $1000$ by $7$ (quotient $142$) and $9999$ by $7$ (quotient $1428$), giving an absolute difference of $|142 - 1428| = 1286$.

Numbers Between $74$ and $25556$ Divisible by $5$

Calculated by dividing $74$ by $5$ (quotient $14$) and $25556$ by $5$ (quotient $5111$), giving an absolute difference of $|5111 - 14| = 5097$.

Numbers Between $100$ and $300$ Divisible by $13$

Calculated by dividing $100$ by $13$ (quotient $7$) and $300$ by $13$ (quotient $23$), giving an absolute difference of $|7 - 23| = 16$.

Numbers Between $300$ and $900$ Divisible by $17$

Calculated by dividing $300$ by $17$ (quotient $17$) and $900$ by $17$ (quotient $52$), giving an absolute difference of $|17 - 52| = 35$.

Do It Yourself Challenge

The practice question posed at the end of the lecture: 'How many three digit numbers are divisible by $11$?'