Type the missing number in this sequence: 1, 2, 5, 10, 17, _____, 37

Question

Type the missing number in this sequence:  1,    2,    5,    10,    17,    _____,    37

Bytelearn · Accepted Answer

Identify Pattern: Identify the pattern in the sequence. We need to determine how each number in the sequence is related to its position in the sequence or to the previous numbers.Examine Differences: Look for a pattern by examining the differences between consecutive terms. The difference between the second and the first term is 2 - 1 = 1. The difference between the third and the second term is 5 - 2 = 3. The difference between the fourth and the third term is 10 - 5 = 5. The difference between the fifth and the fourth term is 17 - 10 = 7. We can see that the differences are consecutive odd numbers: 1, 3, 5, 7...Predict Next Difference: Predict the next difference in the pattern. Following the pattern of increasing by 2 each time (1, 3, 5, 7...), the next difference should be 7 + 2 = 9.Find Missing Number: Add the predicted difference to the last known term to find the missing number. The last known term before the missing number is 17, so we add 9 to it: 17 + 9 = 26.Verify Pattern Continues: Verify the pattern continues correctly after the missing number. The difference between 37 (the term after the missing number) and the missing number (26) should be the next odd number in the sequence, which is 11: 37 - 26 = 11. This confirms that the pattern is correct.

Type the missing number in this sequence: $\newline$ $1$ , $2$ , $5$ , $10$ , $17$ , $\_$ , $37$

Full solution

More problems from Sequences: mixed review

Related topics

Type the missing number in this sequence:\newline111, 222, 555, 101010, 171717, _\__, 373737

Type the missing number in this sequence: $\newline$ $1$ , $2$ , $5$ , $10$ , $17$ , $\_$ , $37$