Contents

- 1 What is the pattern rule for 3 6 10 15?
- 2 What is the nth term of 3 6 9 12 15 18?
- 3 What is the nth term of 1 2 4 7 11?
- 4 What is the nth term rule of 5 2 1 4 7?
- 5 How do you find the nth term of 2 6 10 14 18?
- 6 What is the 15th term of 2 4 6?
- 7 What is the nth term for 5 8 11 14?
- 8 What is the nth term of the sequence 1 5 9 13?
- 9 What is the nth term of 5 7 9 11?

### What is the nth term of 3 5 7 9 11?

Arithmetic Progressions For example: 3, 5, 7, 9, 11, is an arithmetic progression where d = 2. The nth term of this sequence is 2n + 1.

## What is the pattern rule for 3 6 10 15?

Sequences can be linear, quadratic or practical and based on real-life situations. Finding general rules for sequences helps find terms in sequences that would otherwise take a long time to work out.

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Number sequences are sets of numbers that follow a pattern or a rule, Each number in a sequence is called a term, There are some special sequences that you should recognise. The most important of these are:

- square numbers: 1, 4, 9, 16, 25, 36,, – the nth term is \(n^2\)
- cube numbers: 1, 8, 27, 64, 125,, – the nth term is \(n^3\)
- triangular numbers: 1, 3, 6, 10, 15,, (these numbers can be represented as a triangle of dots). The term to term rule for the triangle numbers is to add one more each time: 1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10 etc.
- Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13,, (in this sequence you start off with 1 and then to get each term you add the two terms that come before it)

A sequence which increases or decreases by the same amount each time is called a linear sequence e.g.

### What is the nth term for 2 5 8 11?

Solution: The nth term is 3n – 1.

#### What is the nth term of 15 12 9 6?

Solution: An arithmetic progression is a sequence where the difference between every two consecutive terms is the same. For a given arithmetic sequence, the nth term of AP is calculated using the following expression: a n = a + (n – 1) d Where,

‘a’ is the first term of the AP ‘d’ is the common difference ‘n’ is the number of terms ‘a n ‘ is the n th term of the AP.

Let’s find the nth term of the sequence, 15, 12, 9, 6, Here, a = 15, d = -3, n = n Thus, substituting these values in the formula a n = a + (n – 1) d ⇒ a n = 15 + (n – 1) (-3) ⇒ a n = 15 + 3 – 3n ⇒ a n = 18 – 3n Thus, the expression for the n th term of the sequence, 15, 12, 9, 6, is a n = 18 – 3n.

### What is the rule for 1 3 5 7 9?

This is an arithmetic sequence since there is a common difference between each term, In this case, adding to the previous term in the sequence gives the next term, In other words,, Arithmetic Sequence :

#### What is the rule of 2 4 6 8 10?

Thus, the sequence of even numbers 2, 4, 6, 8, 10, is an arithmetic sequence in which the common difference is d = 2. It is easy to see that the formula for the nth term of an arithmetic sequence is an = a +(n −1)d.

### What is the nth term of 2 4 8 16 32?

So, the next term is: 2 × 2 × 2 × 2 × 2 × 2 = 64.

### What is the nth term of this sequence 1 3 5 7?

Which of the following represents the general term for the sequence 1, 3, 5, 7, 9,,,? 2n – 1, n, n + 2, 2n – Summary: The general term for the sequence 1, 3, 5, 7, 9,,, is 2n – 1.

## What is the nth term of 3 6 9 12 15 18?

Given, A sequence 3,6,9,12. To find, The nth term of the sequence Solution, The first term of the given sequence is 3 and the second term is 6. Let us first calculate the common difference between the term. If a1, a2,a3, a4 are in sequence the common difference is calculated by a2-a1, a3-a2, a4-a3.

- Therefore, the common difference of the sequence 3,6,8,12.
- Is 6 – 3 = 3, 9 – 6 = 3, 12 – 9 = 3.
- Since, the common difference are equal so its clear that the given sequence is an Arithmetic Expression.
- The nth term of the AP is an = a + (n-1)d a = 3 and d = 3 where a is first term of an AP and d is common difference of an AP.

⇒ an = a + (n-1)d ⇒ an = 3 + (n-1)3 ⇒ an = 3 + 3n – 3 ⇒ an = 3n. Hence, nth term of the sequence, 3,6,9,12. is an = 3n.

### What is the sequence 1 1 2 3 5 8?

What is the Fibonacci sequence? – The Fibonacci sequence is a set of integers (the Fibonacci numbers) that starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers. The sequence follows the rule that each number is equal to the sum of the preceding two numbers.

- The Fibonacci sequence begins with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,
- Each number, starting with the third, adheres to the prescribed formula.
- For example, the seventh number, 8, is preceded by 3 and 5, which add up to 8.
- The sequence can theoretically continue to infinity, using the same formula for each new number.

Some resources show the Fibonacci sequence starting with a one instead of a zero, but this is fairly uncommon.

## What is the nth term of 1 2 4 7 11?

Formula and sequence – The maximum number of pieces, p obtainable with n straight cuts is the n -th triangular number plus one, forming the lazy caterer’s sequence (OEIS A000124) The maximum number p of pieces that can be created with a given number of cuts n (where n ≥ 0 ) is given by the formula Using binomial coefficients, the formula can be expressed as Simply put, each number equals a triangular number plus 1. The lazy caterer’s sequence (green) and other OEIS sequences in Bernoulli’s triangle As the third column of Bernoulli’s triangle ( k = 2) is a triangular number plus one, it forms the lazy caterer’s sequence for n cuts, where n ≥ 2. The sequence can be alternatively derived from the sum of up to the first 3 terms of each row of Pascal’s triangle :

k n | 1 | 2 | Sum | ||
---|---|---|---|---|---|

0 | 1 | – | – | 1 | |

1 | 1 | 1 | – | 2 | |

2 | 1 | 2 | 1 | 4 | |

3 | 1 | 3 | 3 | 7 | |

4 | 1 | 4 | 6 | 11 | |

5 | 1 | 5 | 10 | 16 | |

6 | 1 | 6 | 15 | 22 | |

7 | 1 | 7 | 21 | 29 | |

8 | 1 | 8 | 28 | 37 | |

9 | 1 | 9 | 36 | 46 |

This sequence (sequence A000124 in the OEIS ), starting with n = 0, thus results in 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211,, Its three-dimensional analogue is known as the cake numbers, The difference between successive cake numbers gives the lazy caterer’s sequence.

### What is the sequence of 1 3 6 10 15 21?

List Of Triangular Numbers – 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120,136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, and so on.

#### What is the nth term of 9 11 13 15 17?

Summary: An equation for the nth term of the arithmetic sequence 9, 11, 13, 15, is a n = 2n + 7.

### What is the rule of 2 5 8 11 14 17?

The next number in the list of numbers 2, 5, 8, 11, 14,. is 17. Notice that the difference between each consecutive term in this sequence is 3. Therefore, this is an arithmetic sequence with a common difference of 3. Thus, to find the next number in the sequence, we simply add 3 to 14.

## What is the nth term rule of 5 2 1 4 7?

What is the nth term of the sequence 5,2, -1, -4, -7? 8-3n is n’th term for this sequence. It’s an Arithmetic progression.

### What is the nth term formula for 1 3 6 10 15?

Answer and Explanation: 1, 3, 6, 10,. Therefore, the n t h term = n ( n + 1 ) 2.

## How do you find the nth term of 2 6 10 14 18?

The general (nth) term for 2, 6, 10, 14, 18, 22, is 4 and the first term is 2. If we let d=4 this becomes a n =a 1 +(n−1)d. The nth or general term of an arithmetic sequence is given by a n =a 1 +(n−1)d. So in our example a 1 =2 and d=4 so a n =2+(n−1)4=2+4n−4=4n−2.

## What is the 15th term of 2 4 6?

Solution: The arithmetic sequence is: 0, 2, 4, 6, 8, 10, 12, 14? Therefore 15th term in the sequence will be 28.

### What is the nth term of 2 4 8 16 32?

So, the next term is: 2 × 2 × 2 × 2 × 2 × 2 = 64.

## What is the nth term for 5 8 11 14?

The nth term of an A.P.5, 8, 11, 14, is 68.

## What is the nth term of the sequence 1 5 9 13?

Thus, the nth term rule for the given sequence is a n = 4 n − 3.

## What is the nth term of 5 7 9 11?

Formula for the Nth Term of an Arithmetic Sequence – The formula to find the nth term of an arithmetic sequence is a n = a 1 + (n-1)d, where a n is the nth term, a 1 is the 1st term, n is the term number and d is the common difference. To find the formula for the nth term, we need a 1 and d.

- To find the formula for the nth term of an arithmetic sequence, we need to know the difference, ‘d’, and the first term, ‘a 1 ‘.
- In this example, the first term is 5 and the common difference is 2.
- Substituting the values of a 1 = 5 and d = 2 into a n = a 1 + (n-1)d, we get a n = 5 + (n-1)2.
- We simplify this by first expanding the brackets by multiplying (n-1) by 2.

We get a n = 5 + 2n – 2. This simplifies to a n = 2n + 3. : How to Find the Nth Term of an Arithmetic Sequence