Question

17. Ifp" term of an AP is q, q'h term is p. show that rih term is p+q-r

Answer 1

Answer:

The rth term is q + p - r.

Step-by-step explanation:

The nth term of an AP is: $T_{n}=a+(n-1)d$

Here a = first term and d = common difference.

Given:

pth term is q, i.e. $q=a+(p-1)d$...(i)

qth term is p, i.e. $p=a+(q-1)d$...(ii)

Solve (i) and (ii) as follow:

$q=a+(p-1)d\\-p=-a-(q-1)d\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\(q-p)=(p-q)d\\d=\frac{q-p}{-(q-p)}\\d=-1$

The value of a is:

$q=a+(p-1)d\\q=a-(p-1)\\a=q+p-1$

Compute the rth term as follows:

$T_{r}=q+p-1+(r-1)(-1)\\=q+p-1-r+1\\=q+p-r$

Thus, the rth term is q + p - r.