# How do you find the next three terms of the arithmetic sequence 3.1, 4.1, 5.1, 6.1, ...?

Dec 23, 2016

$7.1 , 8.1 , 9.1$

#### Explanation:

The terms of an arithmetic sequence are generated by adding the common difference (d) to the previous term.

${a}_{1} , {a}_{1} + d , {a}_{1} + 2 d , {a}_{1} + 3 d , \ldots . , {a}_{1} + \left(n - 1\right) d$

$\text{where } d = {a}_{2} - {a}_{1} = {a}_{3} - {a}_{2} = \ldots . = {a}_{n} - {a}_{n - 1}$

$\text{here } d = 4.1 - 3.1 = 1$

Adding 1 to each term gives the next 3 terms in the sequence.

$\Rightarrow \left(6.1 + 1\right) = 7.1 \text{ and so on}$