Answered

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If a1 = 6 and an =an-1 -4 then find the value of a4.

Sagot :

Sequences

We know that

[tex]\begin{gathered} a_1_{}^{}=6 \\ a_n=a_{n-1}-4 \end{gathered}[/tex]

We want to find a₄, in order to find it we have to find the previous terms:

a₁, a₂, a₃

In order to find a₂ we use the previous term a₁:

[tex]\begin{gathered} a_1=6 \\ a_2=a_{2-1}-4 \\ =a_1-4 \\ =6-4=2_{} \end{gathered}[/tex]

Similarly, we find a₃

[tex]\begin{gathered} a_2=2 \\ a_3=a_{3-1}-4 \\ =a_2-4 \\ =2-4=-2 \end{gathered}[/tex]

Now we can find a₄, using a₃:

[tex]\begin{gathered} a_3=-2 \\ a_4=a_{4-1}-4 \\ =a_3-4 \\ =-2-4=-6 \end{gathered}[/tex]

Answer: a₄ = -6

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