Question

Give the next two terms in the following sequence:-18, -17, -9, 18, 82, ….

Answer 1

Given

sequence: -18, -17, -9, 18, 82, ….

Solution

The common difference

`d=a_{n+1\text{ }}-a_n`

-17 - (-18) = 1,

-9 - (-17) = 8,

18 - (-9) = 27,

82 - 18 = 64,

Therefore, the difference is a series of cubes of natural numbers,

`\begin{gathered} 1^3=1 \\ 2^3=8 \\ 3^3=27 \\ 4^3=64 \\ 5^3=125 \\ 6^3=216 \end{gathered}`

The cube was added to the term to get next term, check below

`\begin{gathered} -18+1^3=-17 \\ -17+2^3=-9 \\ -9+3^3=18 \\ 18+4^3=82 \\ 82+5^3=207 \\ 207+6^3=423 \end{gathered}`

The final answer

The next two terms in the following sequence: -18, -17, -9, 18, 82, are;

`207,\text{ 423}`