## Does a sequence start at 0 or 1?

Sequences don’t even have to start at 0 or 1, they can start with any number and even be indexed by all integers Z.

**What are mathematical sequences?**

In mathematics, a sequence. A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function. Sequences can be both finite and infinite.

### How do you denote a sequence?

One way to specify a sequence is to list all its elements. For example, the first four odd numbers form the sequence (1, 3, 5, 7). This notation is used for infinite sequences as well. For instance, the infinite sequence of positive odd integers is written as (1, 3, 5, 7.).

**Do all sequences start at 1?**

Sequences can actually start at any number we like. The notation for a sequence with general term an typically is written {eq}\{ a_n…

## Why are mathematical sequences important?

Sequences are useful in a number of mathematical disciplines In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.

**What is geometric sequence in mathematics with example?**

A geometric progression, also known as a geometric sequence, is an ordered list of numbers in which each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio r . Similarly 10,5,2.5,1.25,⋯ 10 , 5 , 2.5 , 1.25 , ⋯ is a geometric sequence with common ratio 12 .

### What is indexedseq in Scala?

Per the Scaladoc, IndexedSeq is “a base trait for indexed sequences. Indexed sequences support constant-time or near constant-time element access and length computation.” In Scala 2.12.4 — which I use for all of the examples that follow — you’ll see that IndexedSeq is actually backed by Vector:

**What is the difference between linear and indexed sequences in Scala?**

These do not add any new operations, but each offers different performance characteristics: A linear sequence has efficient head and tail operations, whereas an indexed sequence has efficient apply, length, and (if mutable) update operations. Frequently used linear sequences are scala.collection.immutable.List and scala.collection.immutable.Stream.

## How are the elements of a sequence indexed?

The elements of a sequence are indexed from zero up to the length of the sequence minus one. The length method on sequences is an alias of the size method of general collections.

**What is indexindexedseq?**

IndexedSeq is a trait. Per the Scaladoc, IndexedSeq is “a base trait for indexed sequences. Indexed sequences support constant-time or near constant-time element access and length computation.”

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