# How do you find an equation that describes the sequence 14, 15, 16, 17,... and find the 16th term?

Mar 17, 2018

color(red)(a_16 = 29

#### Explanation:

Given : ${a}_{1} = 14 , {a}_{2} = 15 , {a}_{3} = 16 , {a}_{4} = 17$

To find the ${16}^{t h}$ term.

We know, common difference $d = {a}_{2} - {a}_{1} = {a}_{3} - {a}_{2} = {a}_{4} - {a}_{3}$

$d = 15 - 14 = 16 - 15 = 17 - 16 = 1$

${n}^{t h}$ term of an Arithmetic Sequence is given by the formula,

${a}_{n} = {a}_{1} + \left(n - 1\right) \cdot d$

${a}_{16} = 14 + \left(16 - 1\right) \cdot 1 = 14 + 15 = 29$