# Find the 7th term in the following sequence: 1, 4, 7, 10, cdots ?

Sep 26, 2016

$\textcolor{g r e e n}{19}$

#### Explanation:

The sequence appears to be an arithmetic sequence with a difference between terms of $\textcolor{b l u e}{3}$.

In general given a first term: $\textcolor{red}{{a}_{1}}$
and a difference between successive terms: ${a}_{n} - {a}_{n - 1} = \textcolor{b l u e}{d}$

the $n$th term can be calculated as ${a}_{n} = \textcolor{red}{{a}_{0}} + \textcolor{b l u e}{d} \cdot \left(n - 1\right)$

Therefore the $7$th term of the given sequence should be
$\textcolor{w h i t e}{\text{XXX}} {a}_{7} = \textcolor{red}{1} + \textcolor{b l u e}{3} \cdot \left(7 - 1\right) = 19$