Question

1 In a sequence of numbers a2 = -3, a3 = -9, a4 = -15. Which equation can be used to find the nth term in the sequence, an?

Answer 1

Notice that there is a common difference in the sequence:

$\begin{gathered} a_2=-3_{} \\ a_3=-9 \\ a_4=-15 \end{gathered}$$\begin{gathered} a_4-a_3=-15--9=-6 \\ a_3-a_2=-9--3=-6 \end{gathered}$

The equation of the nth term of a sequence with first term a_1 and a common difference of d, is:

$a_n=a_1+(n-1)d$

In this case, d=-6. Use n=2 to find a_1:

$\begin{gathered} a_2=a_1+(2-1)d \\ =a_1+d \\ \Rightarrow-3=a_1-6 \\ \Rightarrow a_1=3 \end{gathered}$

Then, the nth term of the sequence is:

$\begin{gathered} a_n=3+(n-1)(-6) \\ =3-6n+6 \\ =9-6n \end{gathered}$

Therefore:

$a_n=9-6n$