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# Coding And Number Series Formulas

## Formulas For Coding And Number Series in Logical

Here , in this Page Formulas For Coding and Number Series is given. We have also covered its types along with questions and answers. Coding questions are very easy to solve once we get to know about the tricks behind them.

**Coding and Number Series Formulas **

Arithmetic Progression | Geometric Progression | |
---|---|---|

Sequence | a, a+d, a+2d,……,a+(n-1)d,…. | a, ar, ar^{2},….,ar^{(n-1)},… |

Common Difference or Ratio | Successive term – Preceding term Common difference = d = a2 – a1 | Successive term/Preceding term Common ratio = r = ar^{(n-1)}/ar^{(n-2)} |

General Term (nth Term) | an = a + (n-1)d | an = ar^{(n-1)} |

nth term from the last term | an = l – (n-1)d | an = l/r^{(n-1)} |

Sum of first n terms | sn = n/2(2a + (n-1)d) | sn = a(1 – rn)/(1 – r) if |r| < 1 sn = a(rn -1)/(r – 1) if |r| > 1 |

**Types of Coding and Number Series **

- Arithmetic Sequences and Series
- Geometric Sequences and Series
- Harmonic Sequences and Series
- Fibonacci Numbers

An **arithmetic series** is a sequence of numbers in which the difference between any two consecutive terms is always the same. This constant difference is called the “common difference.” In other words, an arithmetic series is a sum of the terms in an arithmetic progression.

For example, consider the arithmetic progression: **2, 5, 8, 11, 14, …**

Here, the common difference is **3 (5 – 2 = 3, 8 – 5 = 3, and so on).**

The formula to find the sum of the first n terms of an arithmetic series is given by:

**S_n = n/2 * [2a + (n – 1)d]**

A **geometric series** is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the “common ratio.” In other words, a geometric series is a sum of the terms in a geometric progression.

For example, consider the geometric progression: **2, 6, 18, 54, …**

Here, the common ratio is **3 (6 / 2 = 3, 18 / 6 = 3, and so on).**

The formula to find the sum of the first n terms of a geometric series is given by:

**S_n = a * (1 – r^n) / (1 – r)**

The **harmonic series** is an infinite series that is formed by adding the reciprocals of the natural numbers. It has the following form:

**1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + …**

In other words, the nth term of the harmonic series is given by 1/n. The harmonic series diverges, which means that it does not have a finite sum. As you add more and more terms to the series, the sum keeps getting larger and larger without bound.

The **Fibonacci series** is a sequence of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. **So, the sequence begins: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …**

Mathematically, the Fibonacci series is defined by the recurrence relation:

**F(n) = F(n-1) + F(n-2)**

Where **F(n)** is the nth Fibonacci number, **F(n-1)** is the **(n-1)**th Fibonacci number, and **F(n-2)** is the **(n-2)th** Fibonacci number.

The first few terms of the Fibonacci series are:

**F(0) = 0****F(1) = 1****F(2) = 1****F(3) = 2****F(4) = 3****F(5) = 5****…**

**Coding and Number Series Questions and Answer with Formulas**

**Question 1: **In a certain code ‘NOTE’ is written as ‘TNEO’ and ‘SALE’ is written as ‘LSEA’. How will ‘SEAT’ be written in this code?

**Explanation:**

Here, NOTE = TNEO

SALE = LESA

Analyze the pattern and the set of reasoning trick

SALE => LSEA

On a close examination, we notice;

N-1 O-2 T-3 E-4 => T-3 E-1 N-4 O-2

S-1 A-2 L- 3 E-4 => L-3 S-1 E-4 A-2

So applying the same order to the given word we get-

SEAT as ASTE

**Question 2:**In a certain code ‘5892’ is written as ‘2598’ and ‘2649’ is written as ‘9246’. How will ‘7293’ be written in this code?

**Explanations**

5892 -> 2598

2649 -> 9246

After observing we see 1st is at Second Position , 2nd is at Last Position , 3rd Position remains same , last is at First Position

7293 -> 3792

**Question 3:**In a certain code ‘365’ is written as ‘698’. How will ‘264’ be written in this code?

**Explanation:**

365 – > 698

After Observing we see Each digit increases by 3

so 264 -> 597

**Question 4 :**In a certain code language, if the word ‘GUARDIAN’ is coded as ‘AAIUGRDN’ and ‘ FANTASTIC’ Is coded as ‘ AAIFNTSTC’ Then what is the code for the word ‘GALAXY’ ?

**Explanation: **

In word **GUARDIAN** the vowels are taken first in the same order as they are in the word followed by the consonants So the code becomes **AAIUGRDN**

Similarly, In word **GALAXY** the vowels are taken first in the same order as they are in the word followed by the consonants So the code becomes **AAGLXY.**

**Question 5:**If ARYAN is written as XOVXK , then what is the code of NIKHIL ?

**Explanation :**

Each alphabet of the word is moved 3 steps backward.

In the same way **NIKHIL** will be written as **KFHEFI**

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- Number Series – Questions Formulas | How to Solve Quickly | Tricks & Shortcuts
- Letter and Symbol Series – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Logical Sequence of Words – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Analogy and Classification Pattern – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts

- Number Series – Questions |
- Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Letter and Symbol Series – Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Logical Sequence of Words – Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Analogy and Classification Pattern – Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts

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