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Finding the first terms of the sequence using recursive rule

Finding the first terms of the sequence using recursive rule-example-1
User Azaviruha
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1 Answer

4 votes

Answer:

Given:


a_1=6,a_n=-2a_(n-1),n\ge2

Step 1:

The first term of the sequence will be


a_1=6

Step 2:

To figure out the value of the second term, we will have to put the value of n=2


\begin{gathered} a_n=-2a_(n-1), \\ a_2=-2a_(2-1)=-2a_1 \\ a_2=-2(6) \\ a_2=-12 \end{gathered}

Hence,

The second term of the sequence will be


a_2=-12

Step 3:

To figure out the value of the third term, we will have to put the value of n=3


\begin{gathered} a_n=-2a_(n-1),n=3 \\ a_3=-2(a_(3-1)) \\ a_3=-2a_2,a_2=-12 \\ a_3=-2(-12) \\ a_3=24 \end{gathered}

Hence,

The third term of the sequence will be


a_3=24

Step 4:

To figure out the value of the fourth term, we will have to put the value of n=4


undefined

Hence,

The first four terms of the sequence are 6, -12, 24, -48

User Rogermushroom
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