Question

What is the sum of the first sixteen terms of the arithmetic sequence 1, 5, 9, 13, ... ?

Answer 1

$a \: = \: 1 \: \: \: \: \: \: d \: = \: 5 - 1 \: = \: 4 \: \: \: \: n \: = \: 16$

$S_n\:=\: \frac{n}{2} \: [\: 2a + (n - 1)d] \\ \\ S_{16} \: = \: \frac{16}{2} \: \: \: [2 \: \times 1 + \: (16 - 1)4 ]\\ \\ S_{16} \: = \: \: \: 8 \: \: [ \: 2 \: + 15 \times 4 \: ] \\ \\ S_{16} \: = \: 8 \: [ \: 2 + 60 \: ] \\ \\ S_{16} \: \: = \: 8 \times 62 \\ \\ S_{16} \: \: = \: \: 496$

$\color{aqua}{\underline{ \therefore \:The\:sum\:of\:First\:16\:terms\:of\:the\:given\:ap\:is\:496}}$