Question

The first term of a sequence is the number $n$, and each term thereafter is $5$ greater than the term before. Which of the following is the average (arithmetic mean) of the first nine terms of this sequence?

• A. $n+20$
• B. $n+80$
• C. $2n$
• D. $2n+40$
• E. $9n+180$

Answer 1

The correct option is A $n+20$

The first nine terms of the sequence are:
$n,n+5,n+10,n+15,...,n+40$.
(You should probably write all nine terms out to avoid mistakes.) Adding these terms up gives: $9n+180$.

The average is the sum $(9n+180)$ divided by the number of terms $\left(9\right)$.

The average is then: $\frac{(9n+180)}{9}=n+20$.
Hence, option A is correct.