# How do you write the first five terms of the arithmetic sequence given a_1=15, a_(k+1)=a_k+4 and find the common difference and write the nth term of the sequence as a function of n?

Dec 30, 2017

$15 , 19 , 23 , 27 , 31$; common difference $d = 4$

${a}_{n} = 15 + 4 \left(n - 1\right)$

#### Explanation:

Given: ${a}_{1} = 15 , {a}_{k + 1} = {a}_{k} + 4$

Arithmetic sequence has the form: ${a}_{n} = {a}_{1} + \left(n - 1\right) d$,

where $d$ is the common difference.

Let $k = 1 : \text{ } {a}_{2} = {a}_{1} + 4 = 15 + 4 = 19$

Let $k = 2 : \text{ } {a}_{3} = {a}_{2} + 4 = 19 + 4 = 23$

Let $k = 3 : \text{ } {a}_{4} = {a}_{3} + 4 = 23 + 4 = 27$

Let $k = 4 : \text{ } {a}_{5} = {a}_{4} + 4 = 27 + 4 = 31$

First five terms of the arithmetic sequence: $15 , 19 , 23 , 27 , 31$

common difference: $d = 19 - 15 = 23 - 19 = 27 - 23 = 4$

${a}_{n} = {a}_{1} + \left(n - 1\right) d = 15 + 4 \left(n - 1\right)$