Question

solve this problem 1​

Answer 1

Answer:

HOPE THE ATTACHMENT HELPS YOU

Answer 2

ANSWER:

Let the given G.P be

a , ar , ar² , ar³............ arⁿ

$\small{ \sf{ { t_{(m + n)}}^{th} \to {ar}^{m + n - 1} = p}}$

$\small{ \sf{ t_{{(m - n)}^{th}} \to {ar}^{m - n - 1} = q }}$

→ r²ⁿ = p/q

→ r = (p/q)^½ⁿ

Also,

${ \sf{ {a}^{2} {r}^{2m - 2} = pq }} \\ \small{ \rm{ \implies {ar}^{m - 1} = \sqrt{pq} = {m}^{th}term \: of \: G.P }}$

$\small{ \sf{ {n}^{th} = {ar}^{n - 1} = \frac{p}{ {r}^{m + n - 1} } \times {r}^{n - 1} } } \\ { \rm{ \to {pr}^{ - m} }}$

$\implies p [{\dfrac{q}{p} }] ^{ \frac{m}{2n} }$

Hence proved