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Answer:
The first 5 terms of the sequence are 2, 4, 8, 16 and 32.
Step-by-step explanation:
Given:
[tex]a_{1}[/tex] = 2
[tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] -----------------(i)
To get the first 5 terms of the sequence, substitute in turn, n = 1, 2, 3, 4, 5 into equation (i).
The first term (when n = 1) has been given as:
[tex]a_{1}[/tex] = 2
The second term (when n = 2) is given as:
[tex]a_{2}[/tex] = 2[tex]a_{2-1}[/tex]
[tex]a_{2}[/tex] = 2[tex]a_{1}[/tex] (but [tex]a_{1}[/tex] = 2 )
=> [tex]a_{2}[/tex] = 2(2)
=> [tex]a_{2}[/tex] = 4
The third term (when n = 3) is given as:
[tex]a_{3}[/tex] = 2[tex]a_{3-1}[/tex]
[tex]a_{3}[/tex] = 2[tex]a_{2}[/tex] (but [tex]a_{2}[/tex] = 4 )
=> [tex]a_{3}[/tex] = 2(4)
=> [tex]a_{3}[/tex] = 8
The fourth term (when n = 4) is given as:
[tex]a_{4}[/tex] = 2[tex]a_{4-1}[/tex]
[tex]a_{4}[/tex] = 2[tex]a_{3}[/tex] (but [tex]a_{3}[/tex] = 8 )
=> [tex]a_{4}[/tex] = 2(8)
=> [tex]a_{4}[/tex] = 16
The fifth term (when n = 5) is given as:
[tex]a_{5}[/tex] = 2[tex]a_{5-1}[/tex]
[tex]a_{5}[/tex] = 2[tex]a_{4}[/tex] (but [tex]a_{4}[/tex] = 16 )
=> [tex]a_{5}[/tex] = 2(16)
=> [tex]a_{5}[/tex] = 32
Therefore, the first 5 terms of the sequence are 2, 4, 8, 16 and 32.