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Question
Write the first five terms of the following sequences whose nth terms are:
`a_n = 3^n`
Solution
`a_n = 3^n`
Here, the nth term is given by the above expression. So, to find the first term we use
n = 1 we get
`a_1 = 3^(1)`
= 3
Similarly, we find the other four terms,
Second term (n = 2)
`a_2 = 3^(2)`
= (3)(3)
= 9
Third term (n = 3)
`a_3 = 3^(3)`
= (3)(3)(3)
= 27
Fourth term (n = 4)
`a_4 = 3^(4)`
= (3)(3)(3)(3)
= 81
Fifth term (n = 5)
`a_5 = 3^(5)`
= (3)(3)(3)(3)(3)
= 243
Therefore, the first five terms for the given sequence are
`a_1 = 3, a_2 = 9, a_3 = 27, a_4 = 81. a_5 = 243`
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