Confusion in fraction notation $$a_n = n\dfrac{n^2 + 5}{4}$$

In the above fraction series, for $n=3$ I think the answer should be $26/4$, while the answer in the answer book is $21/2$ (or $42/4$). I think the difference stems from how we treat the first $n$. In my understanding, the first number is a complete part and should be added to fraction, while the book treats it as part of fraction itself, thus multiplying it with $n^2+5$. 
So, I just want to understand which convention is correct.

This is from problem 6 in exercise 9.1 on page 180 of the book Sequences and Series.

Here is the answer sheet from the book (answer 6, 3rd element):


$3,8,15,24,35$
$\dfrac{1}{2},\dfrac{2}{3},\dfrac{3}{4},\dfrac{4}{5},\dfrac{5}{6}$
$2, 4, 8, 16 \text{ and } 32$
$-\dfrac{1}{6},\dfrac{1}{6},\dfrac{1}{2},\dfrac{5}{6},\dfrac{7}{6}$
$25,-125,625,-3125,15625$
$\dfrac{3}{2},\dfrac{9}{2},\dfrac{21}{2},21,\dfrac{75}{2}$
$65, 93$
$\dfrac{49}{128}$
$729$
$\dfrac{360}{23}$
$3, 11, 35, 107, 323$; $3+11+35+107+323+...$
$-1,\dfrac{-1}{2},\dfrac{-1}{6},\dfrac{-1}{24},\dfrac{-1}{120}$; $-1+(\dfrac{-1}{2})+(\dfrac{-1}{6})+(\dfrac{-1}{24})+(d\frac{-1}{120})+...$
$2, 2, 1, 0, -1$; $2+2+1+0+(-1)+...$
$1,2,\dfrac{3}{5},\dfrac{8}{5}$
in elementary school math the fraction $x\frac{y}{z}$ usually means $x+\frac{y}{z}$ and is called a mixed fraction.

However these are almost never used after junior high.

Most of the time when you see $x\frac{y}{z}$ the two terms should be multiplied, so it is equal to $\frac{xy}{z}$.
Here's the Cliff Notes version.  Actually cut and pasted from Cliff Notes:
"•Two variables (letters) next to each other: ab means a times b"

This is always the case, even if the variable is identified as an integer.  If a=3 and b=4 then ab=12, NOT 34.  To understand why 3 1/4 is not 3 x 1/4 it is actually simple - it follows a different rule of notation.  when a number is in front of a fraction they are considered parts of a total number that consists of a whole and a fractional part.
One final example of notation.  Intuitively we know that 34 is thirty-four.  it's not 7, ie 3+4, and it's not 12, ie 3x4.  The notation is our common base 10 system: so 34 is just an abbreviation for (3x10) + (4x1).  Since we do it so often we don't think about it, it's intuitive and we don't look for exceptions.  That's how you should treat ab:  it's a times b always.