This is an arithmetic sequence since there is a common difference between each term. In this case, adding 3 to the previous term in the sequence gives the next term.
This shows that to get to the next term of the sequence, you add 3. Therefore the next term of the sequence is 20.
Its first term = 8 and common difference = 3.
Number sequences are sets of numbers that follow a pattern or a rule. If the rule is to add or subtract a number each time, it is called an arithmetic sequence. If the rule is to multiply or divide by a number each time, it is called a geometric sequence.
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.
2 , 5 , 8 , 11 , 14 , . . . Answer: The sequence is increasing by 3 each time so compare the sequence with the multiples of 3 (3,6,9,12,15...). You will then need to minus 1 from the multiples of 3 to give the numbers in the sequence. So the nth term is 3n - 1.
Rule: xn = n(n-1)/2 + 1
Sequence: 1, 2, 4, 7, 11, 16, 22, 29, 37, ...
This is an arithmetic sequence since there is a common difference between each term. In this case, adding −3 to the previous term in the sequence gives the next term. In other words, an=a1+d(n−1) a n = a 1 + d ( n - 1 ) . This is the formula of an arithmetic sequence.
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 nth term of the sequence 2, 5, 10, 17, 26... ? This is the required sequence, so the nth term is n² + 1. There is no easy way of working out the nth term of a sequence, other than to try different possibilities.
The common difference of the sequence 5,8,11,14 is 3.
Thus, the common difference is 5.
Answer: The 8th term is -19.
Arithmetic sequences
5,8,11,14,17,20,23,26,29,32,35...
What is the nth term of 1/2, 1/3, and 1/4? The pattern is your numerator is always 1 and your denominator increases by one.
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.
What is the Fibonacci sequence? The Fibonacci sequence is a famous group of numbers beginning with 0 and 1 in which each number is the sum of the two before it. It begins 0, 1, 1, 2, 3, 5, 8, 13, 21 and continues infinitely.
Answer. The Fibonacci sequence is the series of numbers: 2, 5, 8, 6, 11, 8 , 13, 21, 34...
The general term for the sequence 1, 3, 5, 7, 9, . . . is 2n - 1.
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 an=a1+(n−1)d. The nth or general term of an arithmetic sequence is given by an=a1+(n−1)d. So in our example a1=2 and d=4 so an=2+(n−1)4=2+4n−4=4n−2.
1, 2, 4, 8, 16, 32, 64, 128, 256, ... This sequence has a factor of 2 between each number. Each term (except the first term) is found by multiplying the previous term by 2.
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, ...
1, 2, 4, 7, 12, 20, 33, 54, 88, ... with offset 1. This sequence counts the number of Fibonacci meanders. A Fibonacci meander is a meander which does not change direction to the left except at the beginning of the curve where it is allowed to make (or not to make) as many left turns as it likes.