Question

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?

Answer 1

`T_n = 5n + 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 + (n-1)d`

`T_n = 6 + (n-1)5`

`T_n = 6 + 5n-5`

`T_n = 5n + 1`