Question

Given the following sequences state the next number 1, 18, 16, 32 ____

1, 1, 2, 3, 5, 8, 13, 21 ____
-26, -15, -4, 7____
256, 225, 196, 169, ____

Answer 1

Not sure about the 1st sequence

Second sequence: 34

Third sequence: 18

Fourth sequence: 144

Explanation:

The second sequence is the Fibonacci sequence. You find the next term by adding to two previous terms, so you have 13+21 which is equal to 34.

The third sequence is an arithmetic sequence that has a common difference of 11. Knowing this, we can add 11 to the last term to find the next one. This gives us 7+11 which is 18

The third sequence is the square of numbers starting form 16 and decreasing by one each time. This can be written with the formula
`t_(n)`=
`(17-n)^2`, where n is the term of the sequence you are solving for. Since you need to solve for the fifth term of the sequence the equation becomes,
`t_(5)`=
`(17-5)^2` which is the same as
`13^2`, so the 5th term is 169.