Question

3, -10, 16, -36, 68, ___-3, 12, -33, 102, -303, ___Identify a pattern in each list of numbers. Then use this pattern to find the next number.

Answer 1

As for the sequence 3,-10,16,-36,68,..., notice that

`\begin{gathered} 3-13=-10 \\ -10+26=-10+2(13)=-10+2^1(13)=16 \\ 16-52=16-4(13)=16-2^2(13)=-36 \\ -36+104=-36+8(13)=-36+2^3(13)=68 \end{gathered}`

Therefore, the next term is

`68-2^4(13)=68-16(13)=-140`

The answer is -140.

Regarding the second pattern, notice that

`\begin{gathered} -3+15=12 \\ 12-45=12-3(15)=12-3^1(15)=-33 \\ -33+135=-33+9(15)=-33+3^2(15)=102 \\ 102-405=102-27(15)=102-3^3(15)=-303 \end{gathered}`

Then, the next term of the sequence is

`-303+3^4(15)=912`

The answer is 912