a

_{1}is the first term in the**sequence**. To find the explicit**formula**, you will need to be given (or use computations to find out) the first term and use that value in the**formula**. r is the common ratio for the**geometric sequence**.What is a series and a sequence?

The list of numbers written in a definite order is called a

**sequence**. The sum of terms of an infinite**sequence**is called an infinite**series**. Therefore**sequence**is an ordered list of numbers and**series**is the sum of a list of numbers.What is an example of a sequence?

Definition and

**Examples**of**Sequences**. A**sequence**is an ordered list of numbers . The three dots mean to continue forward in the pattern established. Each number in the**sequence**is called a term. In the**sequence**1, 3, 5, 7, 9, …, 1 is the first term, 3 is the second term, 5 is the third term, and so on.1

## What is the nth term of a number?

The

**nth Term**. The '**nth**'**term**is a formula with 'n' in it which enables you to find any**term**of a sequence without having to go up from one**term**to the next. 'n' stands for the**term**number so to find the 50th**term**we would just substitute 50 in the formula in place of 'n'.2

## What is a geometric sequence formula?

A

**geometric sequence**is a**sequence**of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.3

## What is GP in maths?

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, is a geometric progression with common ratio 3.

4

## What is the formula for arithmetic series?

+ 1000 which has a constant difference between terms. The first term is a

_{1}, the common difference is d, and the number of terms is n. The sum of an**arithmetic series**is found by multiplying the number of terms times the average of the first and last terms.**Formula**: or.5

## What is the recursive formula for a geometric sequence?

Answer: Recursive formula for a geometric sequence is a

**n**=a**n**−1×r , where r is the common ratio.6

## What is L in arithmetic series?

write

**ℓ**for the last term of a finite**sequence**, and so in this case we would have.**ℓ**= a + (n − 1)d. Key Point. An**arithmetic progression**, or AP, is a**sequence**where each new term after the first is obtained. by adding a constant d, called the common difference, to the preceding term.7

## What is N in a geometric sequence?

For

**geometric sequences**, the common ratio is**r**, and the first term a1 is often referred to simply as "a". Since we get the next term by multiplying by the common ratio, the value of a2 is just: a2 = ar. Continuing, the third term is: a3 =**r**(ar) = ar^{2}.8

## What are arithmetic and geometric sequences?

A sequence is a set of numbers, called terms, arranged in some particular order. An

**arithmetic**sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference. A**geometric**sequence is a sequence with the ratio between two consecutive terms constant.9

## What is the common ratio of a sequence?

The

**common ratio**is the**ratio**between two numbers in a geometric sequence. Keep reading for a detailed definition, the formula for determining the**common ratio**and some example problems. A quiz at the end will allow you to test your knowledge. High School Algebra I: Help and Review /**Math**Courses.10

## What is the formula for the nth term?

Capturing this pattern in alegbra, we write the general (or

**nth**)**term**of an arithmetic sequence as: a_{n}= a_{1}+ (n - 1 ) d. This is the**formula**that will be used when we find the general (or**nth**)**term**of an arithmetic sequence. EXAMPLE 1: Find the general (or**nth**)**term**of the arithmetic sequence : 2, 5, 8, ..11

## What is the common ratio?

For a geometric sequence or geometric series, the

**common ratio**is the**ratio**of a term to the previous term. This**ratio**is usually indicated by the variable r. Example: The geometric series 3, 6, 12, 24, 48, . . . has**common ratio**r = 2.12

## What is the recursive formula?

For a sequence a

_{1}, a_{2}, a_{3}, . . . , a_{n}, . . . a**recursive formula**is a**formula**that requires the computation of all previous terms in order to find the value of a_{n}. Note:**Recursion**is an example of an iterative procedure. See also. Explicit**formula**.13

## What is the geometric series?

A

**geometric series**is a**series**for which the ratio of each two consecutive terms is a constant function of the summation index . The more general case of the ratio a rational function of the summation index produces a**series**called a hypergeometric**series**.14

## What is the formula for an arithmetic sequence?

**Arithmetic Progression**. A

**sequence**such as 1, 5, 9, 13, 17 or 12, 7, 2, –3, –8, –13, –18 which has a constant difference between terms. The first term is a

_{1}, the common difference is d, and the number of terms is n. Explicit

**Formula**: a

_{n}= a

_{1}+ (n – 1)d.

15

## How do you find the common ratio of a geometric sequence?

**Steps**

- Identify the first term in the sequence, call this number a.
- Calculate the common ratio (r) of the sequence. It can be calculated by dividing any term of the geometric sequence by the term preceding it.
- Identify the number of term you wish to find in the sequence. Call this number n.
- The n
^{th}term is given by ar^{n}^{-}^{1}.

16

## What is the formula for arithmetic sequence?

An arithmetic sequence is a sequence in which the difference between each consecutive term is

**constant**. An arithmetic sequence can be defined by an explicit formula in which a_{n}= d (n - 1) + c, where d is the common difference between consecutive terms, and c = a_{1}.17

## What does the summation sign mean?

**Summation Notation**. Often mathematical formulae require the addition of many variables

**Summation**or sigma

**notation**is a convenient and simple form of shorthand used to give a concise expression for a sum of the values of a variable. Let x

_{1}, x

_{2}, x

_{3}, …x

_{n}denote a set of n numbers.

18

## What is a recursive definition for a sequence?

A

**recursive sequence**, also known as a recurrence**sequence**, is a**sequence**of numbers indexed by an integer and generated by solving a recurrence equation. The terms of a**recursive sequences**can be denoted symbolically in a number of different notations, such as , , or f[ ], where is a symbol representing the**sequence**.19

## Can geometric sequence be division?

**Division**as Ratio. The goal of this string is to help students connect multiplication and

**division**in such a way that they

**will**be better able to recognize that to find a common multiplier in a

**geometric sequence**, they

**can use division**. The

**sequences**and the

**division can**be notated (by convention) in different ways.