Question

Show that the sequence defined by $a_n=5n-7$ is an AP. Also, find its common difference.

• A. $-5$
• B. $-1$
• C. $5$
• D. $1$

Answer 1

Answer: (C)

$5$

Here $a_n=5n-7$.
Replacing $n$ by $(n+1)$, we get
$a_{n+1}=5(n+1)-7=5n-2$
Now, $a_{n+1}-a_n=(5n-2)-(5n-7)=5$
Clearly,$a_{n+1}-a_n$ is independent of $n$ and is equal to $5$. So, the given sequence is an AP with common difference $5$.