find the fifth term of the geometric sequence calculator

Issue Sequence Estimator

Arithmetic Sequence Calculator

definition: a_n = a₁ + f × (n-1)
example: 1, 3, 5, 7, 9 11, 13, ...

Geometric Sequence Reckoner

definition: a_n = a × r_n-1
instance: 1, 2, 4, 8, 16, 32, 64, 128, ...

Fibonacci Sequence Calculator

definition: a₀=0; a₁=1; a_n = a_n-1 + a_n-2;
example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

In mathematics, a sequence is an ordered list of objects. Accordingly, a list sequence is an ordered list of numbers that follow a particular pattern. The individual elements in a sequence is often referred to as term, and the number of terms in a episode is called its distance, which can be immortal. In a number sequence, the order of the sequence is important, and depending connected the chronological sequence, it is realistic for the same terms to appear multiple times. There are umteen different types of number sequences, three of the just about informal of which let in arithmetic sequences, geometric sequences, and Fibonacci sequences.

Sequences have many applications in various mathematical disciplines due to their properties of convergence. A series is convergent if the sequence converges to some limit, while a chronological succession that does not converge is divergent. Sequences are used to study functions, spaces, and other mathematical structures. They are particularly useful as a basis for series (essentially key an operation of adding infinite quantities to a starting measure), which are generally misused in differential equations and the country of mathematics referred to as analysis. There are ten-fold slipway to denote sequences, one of which involves simply listing the sequence in cases where the pattern of the episode is easily noticeable. In cases that have more complex patterns, indexing is usually the preferred notation. Indexing involves writing a general formula that allows the determination of the n^th term of a sequence A a function of n.

Pure mathematics Sequence

An arithmetical episode is a amoun sequence in which the difference between to each one successive term cadaver invariable. This difference can either be positive or negative, and dependant on the communicatory will result in terms of the arithmetic chronological succession tending towards positive or harmful infinity. The general form of an arithmetic successiveness can equal written as:

	an = a1 + f × (n-1) or more generally	where an refers to the nth term in the sequence
	an = am + f × (n-m)	a1 is the first full term
i.e.	a1, a1 + f, a1 + 2f, ...	f is the common difference
EX:	1, 3, 5, 7, 9, 11, 13, ...

It is clear in the sequence above that the common deviation f, is 2. Victimisation the equation above to calculate the 5^th term:

X:	a5 = a1 + f × (n-1) a5 = 1 + 2 × (5-1) a5 = 1 + 8 = 9

Looking back at the listed sequence, it give the axe make up seen that the 5th term, a₅ , found using the equating, matches the listed episode as supposed. IT is also commonly desirable, and ovate, to compute the sum of an arithmetic sequence victimization the following recipe in combination with the previous formula to find a_n :

Using the same number episode in the previous example, find the sum of the arithmetic sequence through the 5^th term:

EX:	1 + 3 + 5 + 7 + 9 = 25 (5 × (1 + 9))/2 = 50/2 = 25

Geometric Sequence

A geometric sequence is a number sequence in which each successive numerate after the first number is the multiplication of the past act with a fixed, not-zero number (common ratio). The general form of a geometric sequence ass be written atomic number 3:

	an = a × rn-1	where an refers to the nth terminus in the sequence
i.e.	a, ar, Land of Opportunity2, ar3, ...	a is the weighing machine factor and r is the common ratio
EX:	1, 2, 4, 8, 16, 32, 64, 128, ...

In the example preceding, the commons ratio r is 2, and the descale broker a is 1. Using the equation supra, calculate the 8^th term:

EX:	a8 = a × r8-1 a8 = 1 × 27 = 128

Comparing the prize found using the equation to the geometric sequence above confirms that they match. The equation for calculating the sum of a nonrepresentational sequence:

Using the same geometric sequence above, find the sum of the geometric sequence through the 3^rd term.

EX:   1 + 2 + 4 = 7

Fibonacci Sequence

A Fibonacci sequence is a sequence in which every number followers the first two is the sum of the two preceding numbers. The first two numbers game in a Fibonacci sequence are defined as either 1 and 1, OR 0 and 1 depending on the chosen terminus a quo. Fibonacci numbers pool happen often, as good as unexpectedly within mathematics and are the subject of many studies. They have applications within computer algorithms (much as Euclid's algorithmic rule to compute the superlative common factor), economics, and biological settings including the branching in trees, the flowering of an artichoke, as symptomless as numerous others. Mathematically, the Fibonacci sequence is written as:

	an = an-1 + an-2	where an refers to the natomic number 90 term in the sequence
EX:	0, 1, 1, 2, 3, 5, 8, 13, 21, ...	a0 = 0; a1 = 1

find the fifth term of the geometric sequence calculator

Source: https://www.calculator.net/number-sequence-calculator.html