Question

Suppose that a sequence is defined as follows.a₁ = -1,n=-4an-1+2 for n≥2List the first four terms of the sequence.

Answer 1

We must find the first four terms of a sequence given by the formula

`\begin{gathered} a_n=-4a_(n-1)+2\text{ for n}\ge2 \\ \text{ Considering }a_1=-1 \end{gathered}`

To solve this exercise you just have to do some simple calculations (and logic to find the terms a_(n-1) ):

`\begin{gathered} a_1=-1 \\ a_2=-4(a_1)+2=-4(-1)+2=6 \\ a_3=-4(a_2)+2=-4(6)+2=-22 \\ a_4=-4(a_3)+2=-4(-22)+2=90 \end{gathered}`

Finally, the answer is -1, 6, -22, 90