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.
Answer: The next three terms of the series 2, 5, 10, 17, 26,... are 37, 50, and 65.
Hence 37 is the correct answer.
Hence the correct answer is 50. Air Force Group Y Admit Card Released for 01/2023 intake on 15th February 2023 for Phase 2.
The nth terms: 2,7,12,17,22,27,32,37,42...
Hence the missing number is: 5×5+1 =26.
Answer: Answer is 65. < Previous : Find next number in the series 105, 85, 60, 30, 0, ... Next > : If it takes five minutes to boil one egg, how long ...
2, 5, 10, 17, 26, 37, 50, 65, 82, 101,122,145,170.
The pattern is start at 1 and add consecutive odd numbers to get the next term.
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.
b) The nth term of the sequence 10, 17, 26, 37, 50,... is (n + 2) + 1.
For example, the initial values 3 and 2 generate the sequence 3, 2, 5, 7, 12, 19, 31, 50, 81, 131, 212, 343, 555, ... . The ratio of consecutive terms in this sequence shows the same convergence towards the golden ratio.
2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, ... (sequence A055010 in the OEIS)
Answer and Explanation:
We see that the given sequence is an arithmetic sequence. On putting in those values, we get: a n = 5 + ( n − 1 ) 5 = 5 + 5 n − 5 = 5 n ⟹ a n = 5 n , n = 1 , 2 , …
This is an arithmetic sequence since there is a common difference between each term. In this case, adding −5 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 ) .
an=3n−1.
28 is the missing number in the sequence.
Complete step-by-step solution:
From the sequence we can say that the next term of the sequence $3,4,5,6,7,..... $ will be 8. Therefore, the next term of the sequence $2,5,9,14,20,27,... $ will be $27+8=35$.
Step 1: Find the common difference of each pair of consecutive terms in the sequence by subtracting each term from the term that comes directly after it. Step 2: Add the common difference to the number prior to the first missing number in the sequence. Step 3: Repeat Step 2 for any other missing numbers.
Formula and sequence
Simply put, each number equals a triangular number plus 1. 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. 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, ...
Example: 3, 5, 8, 13, 21, ? After 3 and 5 all the rest are the sum of the two numbers before, That is 3 + 5 = 8, 5 + 8 = 13 etc, which is part of the Fibonacci Sequence: 3, 5, 8, 13, 21, 34, 55, 89, ...