# How do you find the nth term formula 4, 4.3, 4.6, 4.9?

Jul 1, 2016

${a}_{n} = 4 + 0.3 \left(n - 1\right)$

#### Explanation:

The difference between each term is 0.3 so we have an arithmetic sequence.

Let $i$ be the term position count in the sequence
Let any term be ${a}_{i}$

Then
$i \to {a}_{1} = 4$
$i \to {a}_{2} = 4 + 0.3$
$i \to {a}_{3} = 4.6 = 4 + \left(2 \times 0.3\right)$
$i \to {a}_{4} = 4.9 = 4 + \left(3 \times 0.3\right)$

We observe that any term ${a}_{i} = 4 + \left[\left(i - 1\right) \times 0.3\right]$

Thus for $i = n$ we have ${a}_{n} = 4 + \left[\left(n - 1\right) \times 0.3\right]$

Write as:$\text{ } {a}_{n} = 4 + 0.3 \left(n - 1\right)$