The next number in the sequence is 26, and the general formula is 𝑎 𝑛 = 𝑛 2 + 1 𝐚 𝐧 = 𝐧 𝟐 + 𝟏 .
Let's find the differences between consecutive terms: 5 - 2 = 3, 10 - 5 = 5, 17 - 10 = 7. The differences between the terms are not constant, so this is not an arithmetic sequence. However, the differences themselves (3, 5, 7) do increase by a constant amount (2), suggesting that this could be a quadratic sequence.
This pattern in the series can be seen below. So, the missing number of the series will be 65.
Given series: 2, 5, 10, 17, 26, ? Hence, 37 is correct.
The 7th term of the sequence is 50.
Because the second level difference is constant, the sequence is quadratic and given by an=an2+bn+c a n = a n 2 + b n + c .
Think prime numbers. The next number is found by adding the next prime number to the current number. 5 5 + 5 = 10 10 + 7 = 17 17 + 11 = 28 28 + 13 = 41 41 + 17 = 58 58 + 19 = 77 77 + 23 = 100 100 replaces the ? Deomani Sharma Ramsurrun The solution is 77+23=100.
Therefore, according to this logic, the missing number is 26.
Answer: The next three terms of the series 2, 5, 10, 17, 26,... are 37, 50, and 65.
The explicit formula for the nth term of an arithmetic sequence is an = a1 + d(n - 1), where an is the nth term of the sequence, a1 is the first term of the sequence, and d is the common difference of the sequence.
Hence, we have found the common difference of the arithmetic sequence 5, 9, 13, 17,.... The common difference is 4.
Hence the sequence is 2 , 5 , 10 , 17 , 26 , 37 , 50 , 65 . Note: As we discussed earlier, there can be multiple patterns to this question. Another pattern behind this sequence is that each term can be given by the formula n 2 + 1 .
Starting from the second term (5), we add consecutive odd numbers: 3, 5, 7, 9, 11, 13. Therefore, the 9th term in the sequence is 75.
Sequences are ordered lists of numbers (called "terms"), like 2,5,8. Some sequences follow a specific pattern that can be used to extend them indefinitely. For example, 2,5,8 follows the pattern "add 3," and now we can continue the sequence. Sequences can have formulas that tell us how to find any term in the sequence.
123 + 4 - 5 + 67 - 89 = 100.
Here are the rules: use every digit in order - 123456789 - and insert as many addition and subtraction signs as you need so that the total is 100. Remember the order of operations!
What is a sequence? A number sequence is a set of numbers that follow a particular pattern or rule to get from term to term. There are four main types of different sequences you need to know, they are arithmetic sequences, geometric sequences, quadratic sequences and special sequences.
To find the next two terms of the sequence 2,5,10,17, we first look for a pattern in the differences between consecutive terms. The differences are as follows: 5−2=3, 10−5=5, 17−10=7. The differences are 3,5,7, which form an arithmetic sequence with a common difference of 2.
Explanation. The given sequence is: 2, 5, 10, 17, 28, 41.
The correct Answer is: To find the next term in the series: 2, 5, 10, 17, 26, 37, 50, 64, we will analyze the pattern in the sequence step by step.
Finding a Term in the Sequence
By knowing the first term (a₁), the common difference (d), and the position of the term (n), you can calculate the nth term using the formula: aₙ = a₁ + (n – 1)d. This formula enables you to find any term within the sequence without having to manually calculate each preceding term.
Answer: The expression to calculate the nth term of an arithmetic sequence is an = a + (n - 1) d. Where, 'a' is the first term of the AP. 'd' is the common difference.
Thus, the expression for the nth term of the sequence, 15, 12, 9, 6, … is an = 18 - 3n.