Question

Find the missing term in the following sequence ? 1, 4, 11, 26, 57, 120, ______

Answer 1

247

Explanation:

1,4,11,26,57,120. see the pattern that emerges from the series:

4–1 = 3; 3–1 = 2 = 2^1

11–4 = 7; 7 - 3 = 4 = 2^2

26 - 11 = 15; 15 - 7 = 8 = 2^3

57 - 26 = 31; 31 - 15 = 16 = 2^4

120 - 57 = 63; 63 - 31 = 32 = 2^5

so the next number should be 64+63 = 127+120 = 247.

check: 247–120 = 127; 127–63 = 64 = 2^6. correct.

so the next number is 247. 2^n+(n-1)

Answer 2

Given sequence;

1, 4, 11, 26, 57, 120, _

The missing term =?

Solution;

We need to find the relationship between each term and then we can find the missing term;

1, 4, 11, 26, 57, 120, _ ;

let us start with the first two;

3 x 2 + 1 = 7 + 4 = 11

7 x 2 + 1 = 15 + 11 = 26

15 x 2 + 1 = 31 + 26 = 57

31 x 2 + 1 = 63 + 57 = 120

63 x 2 + 1 = 127 + 120 = 247

We see this pattern and can conclude that the missing term is 247