# Equations of conic sections, Systems of Non-linear Equations illustrate a series, differentiate a series from a sequence Determine the first five terms of each defined sequence and give it's associated series 3^{n + 1} We have to find the first five terms of the given sequence and its associated series

Question
Conic sections
Equations of conic sections, Systems of Non-linear Equations illustrate a series, differentiate a series from a sequence Determine the first five terms of each defined sequence and give it's associated series $$3^{n\ +\ 1}$$ We have to find the first five terms of the given sequence and its associated series

2021-01-20
Given that, $$n^{th}\ \text{term of the sequence is}\ 3^{n\ +\ 1}.$$ Take $$n = 0$$ $$a_{n} = 3^{n\ +\ 1}$$
$$a_{0} = 3^{0\ +\ 1} = 3$$ Therefore, the first term is 3. Take $$n = 1,$$
$$a_{1} = 3^{1\ +\ 1}$$
$$a_{1} = 3^{1\ +\ 1} = 3^{2} = 9$$ The second term is 9 Take $$n = 2,$$
$$a2 = 3^{2\ +\ 1}$$
$$= 3^{3}$$
$$a_{2} = 27$$ The third term is 27 For, $$n = 3,$$
$$a3 = 3^{3\ +\ 1}$$
$$= 3^{4}$$
$$a^{3} = 81$$ Fourth term is 81 For, $$n = 4,$$
$$a4 = 3^{4\ +\ 1}$$
$$= 3^{5}$$
$$a^{4} = 243$$ Fifth term is 243. Therefore, the first 5 terms of the sequence are $$3,\ 9,\ 27,\ 81,\ 243.$$ Step 3 The given sequence is $$3,\ 9,\ 27,\ 81,\ 243.$$ The series associated with the given sequence is $$\sum_{n=0}^{5}\ 3^{n\ +\ 1}=3\ +\ 9\ +\ 27\ +\ 81\ +\ 23$$
$$\sum_{n=0}^{5}\ 3^{n\ +\ 1}=363$$

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