Question

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

$\left\{s_n\right\}=\left\{n+4\right\}$

Short answer

The solution is $d=1$; first four terms$=5,6,7,8$.

Step-by-step solution

Step 1. Given information 

$\left\{s_n\right\}=\left\{n+4\right\}$

Step 2. Calculation 

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

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

$s_n=n+4$ and $s_{n-1}=n-1+4=n+3$

The common difference is -

$d=s_n-s_{n-1}=\left(n+4\right)-\left(n+3\right)=1$

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 localid="1649240847390" $5,6,7$and 8.