# .What is x if the sequence 1,5, 2x+3 ....is an arithmetic sequence?

Jul 20, 2016

$x = 3$

#### Explanation:

If the sequence is arithmeic, then there is common difference between the consecutive terms.

$d = {T}_{3} - {T}_{2} = {T}_{2} - {T}_{1}$

$\left(2 x + 3\right) - 5 = 5 - 1 \text{ we have an equation - solve it}$

$2 x = 4 - 3 + 5$

$2 x = 6$

$x = 3$

The sequence would be

$1 , 5 , 9$ There is a common difference of 4.