Sequence and Series Formulas

Sequence and Series Formulas

Sequence And Series Formulas is very necessary for students to practice questions. Students will get all the explanations about the Sequence And Series Formulas on Extramarks. The live classes available on Extramarks will help students to score well in the upcoming examinations. Every question involving the Sequence And Series Formulas can be easily solved by referring to the NCERT solutions provided by Extramarks. It is crucial for students to keep revising each topic of sequence and series, along with the Sequence And Series Formulas. Students having doubts and confusion about the Sequence And Series Formulas must take guidance from the teachers at Extramarks. 

What are Sequences and Series Formulas?

Mathematical sequence and series formulae pertain to several kinds of sequences and series. A series is the accumulation of elements in a sequence, which is a group of arranged elements that follow a pattern. The formulae for the nth term and the sum are typically included in the sequence and series formulas. The arithmetic, geometric, and harmonic sequences are covered in the list of sequences and series formulas that follow. Here, formulas for the sequence and series are included.

Formulae are used to determine the total of the n terms in the series, as well as the nth term in the sequence. There is a shared difference between two successive terms in an arithmetic series. An average ratio exists between succeeding terms in a geometric sequence. The reciprocals of the terms in a harmonic sequence are in an arithmetic sequence.

Arithmetic Sequence and Series Formulas

An arithmetic sequence is one in which each phrase is produced by either adding or subtracting a specific number from the number before it. An ordered list of numbers is termed a sequence. The sequence’s terms are represented by the numbers in the list. A series is created by adding each term in a sequence. Series and sequences are analogous to sets, however, a sequence differs from a series in that a single term may appear several times in different positions. A sequence’s length is equal to its term count, which may be limited or infinite. It is crucial to know that a sequence is an ordered list of numbers. The numbers in the list are the terms of the sequence. The terms of a sequence usually name ai  or an with the subscripted letter i or n being the index. So, the second term of a sequence might be named a2, and a12 would be the twelfth term.

Geometric Sequence and Series Formulas

A geometric sequence is one where each phrase is produced by multiplying or dividing a certain integer by the one before it.

Harmonic Sequence and Series Formulas

A series of numbers is said to be in a harmonic sequence if all of their reciprocals can be expressed as an arithmetic sequence. When attempting to perform predictive or projective computations, sequences and series are of utmost importance. While watching a cricket play, one straightforward example is score prediction, needed run rate, anticipated score, etc. To visualise a future score that is a few steps further in the expansion of the sequence that was noticed from previous scores, all of these computations are akin to examining numerical patterns and extending or summing them up.

The following term can be obtained by multiplying the values of the two words that come before the necessary term. The Fibonacci sequence is one such sort of series. No discernible pattern is present. The Fibonacci sequence is named after the well-known Italian mathematician Leonardo Fibonacci. The Fibonacci sequence is well-known because it has a pattern with numerous other natural wonders, like the shapes of eggs and flower petals. The golden ratio, a crucial element in design and photography, is also determined using this procedure.

Examples on Sequences and Series Formulas

All the examples based on the Sequence And Series Formulas should be practised by students. They are advised to practice more on more questions to learn the implementation of the Sequence And Series Formulas. Practising questions with the Sequence And Series Formulas is important for understanding the topics in depth.