# How do you write the first five terms of the arithmetic sequence given a_1=6, a_(k+1)=a_k+5 and find the common difference and write the nth term of the sequence as a function of n?

Mar 8, 2017

${T}_{n} = 5 n + 1$

#### Explanation:

common different, $d = {a}_{n} - {a}_{n - 1}$

Therefore,
$d = {a}_{k + 1} - {a}_{k} = {a}_{k} + 5 - {a}_{k} = 5$

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

${T}_{n} = 6 + \left(n - 1\right) 5$

${T}_{n} = 6 + 5 n - 5$

${T}_{n} = 5 n + 1$