A tiny uncertainty on estimation

Problem :

If the amount of the first $p$ regards to a math development is $q$ and also the amount of the first $q$ terms is $p$, after that locate the amount of $p+q$ terms.

For the trouble we can write (taking into consideration $a$ is the first term and also $d$ is the usual distinction) :

$$\frac{p}{2}\cdot \biggl[2a + (p-1)d \biggr] = q \qquad \cdots (1)$$

$$\frac{q}{2}\cdot \biggl[2a + (q-1)d \biggr] = p \qquad \cdots (2)$$

Now in my component it is considered that from these we can write $\displaystyle d= \frac{-2(p+q)}{pq}$ ; I am not obtaining just how we can get that value of $d$?!

2019-12-02 02:51:03
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Answers: 2

$q \times (1) - p \times (2)$ will certainly offer you $d$ and afterwards you can exercise $a.$

2019-12-03 04:13:24

You get 2 formulas in 2 unknowns $a,d$ ; address them to locate $d$. Given that we just intend to locate $d$, we can relate the coefficient of $a$ by increasing the first formula by $q$, the 2nd by $p$, and also deducting to get a straight formula for $d$.

2019-12-03 04:13:21