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Normally I wouldn't post the question straight out of the book, but today I am desperate because I just cannot get any bearing on this one.
Triangular numbers of objects can be arranged to form triangles. The first four triangle numbers are: 1, 3, 6, 10.
a)an expression to find the nth triangular number can be written in the form n(n+p)/q where p and q represent whole numbers. Complete the expression by determining the numbers represented by p and q.
Well, the first triangular number is $\displaystyle 1$ so:Quote:
Originally Posted by mike_302
$\displaystyle 1(1+p)/q=1$
and the second is $\displaystyle 3$, so:
$\displaystyle 2(2+p)/q=3$
Hence:
$\displaystyle q-p=1$
and
$\displaystyle 3q-2p=4$
so $\displaystyle q=2$, and $\displaystyle p=1$.
Hence $\displaystyle T_n=\frac{n(n+1)}{2}$
RonL
Sorry, It was explained simply, and I like that, but you lost me at:
Hence: q-p=1 ... I do not understand how you obtained that.
The first equation I had was $\displaystyle 1(1+p)/q=1$, now assuming $\displaystyle q \ne 0$ this becomes on multiplying through by $\displaystyle q$:Quote:
Originally Posted by mike_302
$\displaystyle 1+p=q$
which is then rearranged to give $\displaystyle q-p=1$
RonL
