Each number is got by adding an amount two larger than the last amount added. 9 (+3) 12 (+5) 17 (+7) 24.
Continuing this we get 33, 44 and 57.
To find the next three terms in the sequence 9, 12, 17, 24, we first identify the differences between consecutive terms: 12 - 9 = 3, 17 - 12 = 5, and 24 - 17 = 7. The differences themselves form an increasing arithmetic sequence: 3, 5, 7. Continuing this pattern, the next differences would be 9, 11, and 13, leading to the subsequent terms being 24 + 9 = 33, 33 + 11 = 44, and 44 + 13 = 57. Therefore, the next three terms are 33, 44, and 57.
To find the first three terms of an arithmetic sequence with a common difference of -5, we first need the last term. If we denote the last term as ( L ), the terms can be expressed as ( L + 10 ), ( L + 5 ), and ( L ) for the first three terms, since each term is derived by adding the common difference (-5) to the previous term. Thus, the first three terms would be ( L + 10 ), ( L + 5 ), and ( L ).
To find the first three terms of a sequence where the fifth term is 162, we can assume the sequence follows a specific pattern, such as an arithmetic sequence. For example, if we let the first term be ( a ) and the common difference be ( d ), the fifth term can be expressed as ( a + 4d = 162 ). By choosing ( a = 82 ) and ( d = 20 ), the first three terms would be 82, 102, and 122. However, many sequences could satisfy the condition, so the terms can vary depending on the assumed pattern.
6
Three or more terms of a sequence are needed in order to find its nth term.
1, -3, -7
The sequence 9, 9, 9, 9 is an arithmetic sequence with a common difference of 0. Therefore, the next three terms of the sequence are also 9, 9, and 9.
To find the first three terms of an arithmetic sequence with a common difference of -5, we first need the last term. If we denote the last term as ( L ), the terms can be expressed as ( L + 10 ), ( L + 5 ), and ( L ) for the first three terms, since each term is derived by adding the common difference (-5) to the previous term. Thus, the first three terms would be ( L + 10 ), ( L + 5 ), and ( L ).
27,33,39
This sequence is an arithmetic series that makes use of another series. This sequence advances by adding the series 4, 11, 21, 34, and 50 to the initial terms. This secondary series has a difference of 7, 10, 13 and 16 which advance by terms of 3. So the next three numbers in the primary sequence are 190, 281 and 397.
Which sequence? Oh, that one! The first three terms are 1, 2 and 72.
6
It is an arithmetic sequence. To differentiate arithmetic from geometric sequences, take any three numbers within the sequence. If the middle number is the average of the two on either side then it is an arithmetic sequence. If the middle number squared is the product of the two on either side then it is a geometric sequence. The sequence 0, 1, 1, 2, 3, 5, 8 and so on is the Fibonacci series, which is an arithmetic sequence, where the next number in the series is the sum of the previous two numbers. Thus F(n) = F(n-1) + F(n-2). Note that the Fibonacci sequence always begins with the two numbers 0 and 1, never 1 and 1.
three
Each number in the sequence is 8 times the previous term, hence the next three terms are: 204.8, 1638.4 and 13107.2
Three or more terms of a sequence are needed in order to find its nth term.
-2,-4,-6.