Question

In the problem, show that each sequence is arithmetic. Find the common difference and write out the first four terms.

$\left\{s_n\right\}=\left\{n-5\right\}$

Short answer

The solution is$d=1$; first four terms $=-4,-3,-2,-1$.

Step-by-step solution

Step 1. Given information 

$\left\{s_n\right\}=\left\{n-5\right\}$

Step 2. Calculation 

The first term is $s_1=1-5=-4$.

The $n$th term and the $\left(n-1\right)$st term of the sequence are-

$s_n=n-5$ and $s_{n-1}=n-1-5=n-6$

The common difference is -

$d=s_n-s_{n-1}=\left(n-5\right)-\left(n-6\right)=1$

Since the difference of any two successive terms is the constant $1$, the sequence $\left\{s_n\right\}$is arithmetic.

The first four terms are$-4,-3,-2,-1$.