1.) Find the sum of the first 5 terms of the geometric sequence 1, 4, 16,...

Formula: [tex]Sn= \frac{a_{1} (1-r {}^{n)}}{1 - r} [/tex]

Where, a1=1, r=4, n=5 To find the r u simply just take [tex]r = \frac{a_{1} }{a_{2} } = \frac{1}{4} = 2[/tex]

Solution:

[tex]Sn= \frac{a_{1}(1- r {}^{n})}{1 - r} [/tex]

[tex]S_{5}= \frac{1( 1 - {4}^{5}) }{1 - 4} [/tex]

[tex]S_{5} = \frac{1(1 - 1024)}{1 - 4} [/tex]

[tex]S_{5} = \frac{1( - 1023)}{ - 3} [/tex]

[tex]S_{5} = \frac{ - 1023}{ - 3} [/tex]

[tex]S_{5} = 341[/tex]