# How do you write the first five terms of the arithmetic sequence given a_1=200, a_(k+1)=a_k-10 and find the common difference and write the nth term of the sequence as a function of n?

Jun 8, 2017

First ffive terms are $\left\{200 , 190 , 180 , 170 , 160\right\}$. Common difference is $10$ and ${n}^{t h}$ term ${a}_{n} = 210 - 10 n$

#### Explanation:

As ${a}_{k + 1} = {a}_{k} - 10$, this means that

each succeeding term is $10$ less than the previous term.

Hence $d$ the common difference is given by $d = - 10$

Now first term ${a}_{1}$ is $200$ and as ${n}^{t h}$ term is given by $a + \left(n - 1\right) d = 200 + \left(n - 1\right) \times \left(- 10\right) = 200 - 10 n + 10 = 210 - 10 n$

and hence ${a}_{2} = {a}_{1} - 10 = 200 - 10 = 190$

${a}_{3} = {a}_{2} - 10 = 190 - 10 = 180$

${a}_{4} = {a}_{3} - 10 = 180 - 10 = 170$

qnd ${a}_{5} = {a}_{4} - 10 = 170 - 10 = 160$

Hence first ffive terms are $\left\{200 , 190 , 180 , 170 , 160\right\}$.