# Which of the following is the algebraic expression that best describes the sequence 7,14, 21, 28,?

Jan 26, 2018

${a}_{n} = 7 n$

#### Explanation:

$\text{the terms are the terms of an "color(blue)"arithmetic sequence}$

$a , a + d , a + 2 d , \ldots \ldots , a + \left(n - 1\right) d$

$\text{where a is the first term and d the common difference}$

$a + \left(n - 1\right) d \text{ is the n th term}$

$\text{here } d = 28 - 21 = 21 - 14 = 14 - 7 = 7$

$\Rightarrow {a}_{n} = 7 + 7 \left(n - 1\right) = 7 n$

$\Rightarrow {a}_{n} = 7 n \text{ generates the terms in the sequence}$