# How do you write the first five terms of the arithmetic sequence given a_1=-.375, a_(k+1)=a_k+0.25 and find the common difference and write the nth term of the sequence as a function of n?

Feb 22, 2018

First $5$ terms of arithmatic sequence is
$\left\{- 0.375 , - 0.125 , 0.125 , 0.375 , 0.625\right\} \mathmr{and} n$ th term of the arithmatic sequence is ${a}_{n} = - 0.375 + \left(n - 1\right) 0.25$

#### Explanation:

${a}_{1} = - 0.375 , {a}_{k + 1} = {a}_{k} + 0.25$. Common difference

is d= a_(k+1)-a_k ; a_(k+1)-a_k= 0.25 :. d= 0.25

First term is ${a}_{1} = - 0.375$

Second term is ${a}_{2} = {a}_{1} + d = - 0.375 + 0.25 = - 0.125$

Third term is ${a}_{3} = {a}_{1} + 2 d = - 0.375 + 2 \cdot 0.25 = 0.125$

Fourth term is ${a}_{4} = {a}_{1} + 3 d = - 0.375 + 3 \cdot 0.25 = 0.375$

Fifth term is ${a}_{5} = {a}_{1} + 4 d = - 0.375 + 4 \cdot 0.25 = 0.625$

First $5$ terms of arithmatic sequence is

$\left\{- 0.375 , - 0.125 , 0.125 , 0.375 , 0.625\right\}$

$n$ th term of arithmatic sequence is ${a}_{n} = {a}_{1} + \left(n - 1\right) d$ or

${a}_{n} = - 0.375 + \left(n - 1\right) 0.25$ [Ans]