Question

Express the series in summation notation.

2 + 4 + 6 + 8 + 10 + 12

Answer 1

ANSWER

$\sum _{n = 1} ^{6} 2n$

EXPLANATION

The series is:

2 + 4 + 6 + 8 + 10 + 12

The first term is:

f(1)=2

The common difference is

$d= 4 - 2 = 2$

The formula for the corresponding sequence is

$f(n) = 2 + 2(n - 1)$

$f(n) = 2 + 2n - 2$

$f(n) = 2n$

The summation notation is:

$\sum _{n = 1} ^{6} 2n$