4,11,22,37

Find an expression, in terms of n, for the nth term of this sequence.

Answer: Nth = T + (n + 4)

Step-by-step explanation:

By adding the difference between each number by 4 and in turn, add it to the previous number. For example, the difference of 11 and 4 is 7. Then, you add 4 to the difference which is 3 which becomes 7. Use that 7 and add it to the previous number, which is 4, to become 11. Now, find the difference between 11 and 4 and you find that its 7. Then, you add 4 to 7 to become 11 and use 11 to add to your previous number, which is 11 to become 22. Use the same method to find 37 and the other nth terms.

In maths terms,

3+4 = 7 (4+7 = 11)

7+4 = 11 (11+11 = 22)

11+4 = 15 (22+15 = 37)

So, the formula is,

Nth = T + (n + 4) where n = - 1, 3, 7, 11, etc ... and T=previous term

4 = 1 + (-1 + 4)

11 = 4 + (3 + 4)

22 = 11 + (7 + 4)

37 = 22 + (11 + 4)