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Equations of conic sections, Systems of Non-linear Equations illustrate a series, differentiate a series from a sequence Determine the first five term

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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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