Step 1: The nth term of an arithmetic sequence is given by **an = a + (n – 1)d**. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.

Step 1: The nth term of an arithmetic sequence is given by **an = a + (n – 1)d**. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.

To establish a rule for a number pattern involving ordered pairs of x and y, we can **find the difference between every two successive values of y**. If the difference pattern is the same, then the coefficient of x in the algebraic rule (or formula) is the same as the difference pattern.

Few examples of numerical patterns are: **Even numbers pattern** -: 2, 4, 6, 8, 10, 1, 14, 16, 18, … Odd numbers pattern -: 3, 5, 7, 9, 11, 13, 15, 17, 19, … Fibonacci numbers pattern -: 1, 1, 2, 3, 5, 8 ,13, 21, … and so on.

A linear number pattern is a list of numbers in which the difference between each number in the list is the same. The formula for the nth term of a linear number pattern, denoted an, is **an = dn - c**, where d is the common difference in the linear pattern and c is a constant number.

A numerical pattern is **a sequence of numbers that has been created based on a rule called a pattern rule**. Pattern rules can use one or more mathematical operations to describe the relationship between consecutive numbers in the sequence.

An arithmetic Sequence is a set of numbers in which each new phrase differs from the previous term by a fixed amount. Geometric Sequence is a series of integers in which each element after the first is obtained by multiplying the preceding number by a constant factor.

Pattern Rules. A numerical pattern is a sequence of numbers that has been created based on a formula or rule called a **pattern rule**. Pattern rules can use one or more mathematical operations to describe the relationship between consecutive numbers in the pattern.

Arithmetic Sequence and Series Formulas

Sum of the arithmetic series, **S _{n} = n/2 (2a + (n - 1) d)** (or) S

To find the number of terms in an arithmetic sequence, **divide the common difference into the difference between the last and first terms, and then add 1**.

Types of Arithmetic sequence**Finite Sequence**- Finite sequences have countable terms and do not go up to infinity. An example of a finite arithmetic sequence is 2, 4, 6, 8. Infinite Sequence- Infinite arithmetic sequence is the sequence in which terms go up to infinity.

**Hands On Practice with Number Patterns**

- Use buttons or counters on ten frames or ten towers to show how increasing or decreasing numbers form a pattern.
- Talk about how each ten frame has "1 more" counter than the last.
- Show how 11 and 1 more makes 12, 12 and 1 more makes 13, 13 and 1 more makes 14 and so on.

**Arithmetic Progression (AP)**

- nth term of an AP = a + (n-1) d.
- Arithmetic Mean = Sum of all terms in the AP / Number of terms in the AP.
- Sum of 'n' terms of an AP = 0.5 n (first term + last term) = 0.5 n

The arithmetic sequence formula is given as, **an=a1+(n−1)d** a n = a 1 + ( n − 1 ) d where, an a n = a general term, a1 a 1 = first term, and and d is the common difference. This is to find the general term in the sequence.

To establish a rule for a number pattern involving ordered pairs of x and y, we can **find the difference between every two successive values of y**. If the difference pattern is the same, then the coefficient of x in the algebraic rule (or formula) is the same as the difference pattern.

sequence determined by a = 2 and d = 3. Solution: To find a specific term of an arithmetic sequence, we use the formula for finding the nth term. Step 1: The nth term of an arithmetic sequence is given by **an = a + (n – 1)d**. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.

Number pattern is **a pattern or sequence in a series of numbers**. This pattern generally establishes a common relationship between all numbers. For example: 0, 5, 10, 15, 20, 25, … Here, we get the numbers in the pattern by skip counting by 5.

Arithmetic Sequence and Series Formulas

Sum of the arithmetic series, **S _{n} = n/2 (2a + (n - 1) d)** (or) S

**Types of Sequence and Series**

- Arithmetic Sequences.
- Geometric Sequences.
- Harmonic Sequences.
- Fibonacci Numbers.

Solution: To find a specific term of an arithmetic sequence, we use the formula for finding the nth term. Step 1: The nth term of an arithmetic sequence is given by **an = a + (n – 1)d**. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula.

7-8 year olds can **create and continue number patterns and relate these to addition and subtraction to 20**. Patterns can be linked to strategies such as skip counting. Most children at this age can skip count to 100 and identify the pattern, skip counting by 2s, 4s and 5s.

Dated : 03-Jun-2022

Category : Education