Question

in a gp if 2p th term = q^2 and 2q th term = p^2 then (p+q) th term = ​

Answer 1

Answer:

pq

Step-by-step explanation:

Let Ft=a and ration=r

then

A2p=ar^(2p-1)=q²-------------(1)

A2q=ar^(2q-1)=p²-------------(2)

Multiplying (1) by (2)

a²r^{2p-1+(2q-1)}=p²q²

a²r^{2(p+q-1)}= p²q²

[ar^(p+q-1)]²=(pq)²

ar^(p+q-1)=pq

Hence (p+q) th term=pq

Answer 2

The (p+q)th term is pq.

Explanation:

The nth term in G. P . = $T_n=ar^{n-1}$

So , 2pth term =  $T_{2p}=ar^{2p-1}= q^2$

2 qth term =  $T_{2q}=ar^{2q-1}= p^2$

Now , Consider $T_{2p}\times T_{2q}$

$ar^{2p-1}\times ar^{2q-1} =q^2\times p^2$

$a^2r^{2p-1+(2q-1)} = p^2q^2$  [∵ $a^m\times a^n = a^{m+n}$]

$a^2r^{2p-1+2q-1} = p^2q^2$

$a^2r^{2p+2q-2} = p^2q^2$

$a^2r^{2(p+q-1)} = p^2q^2$

$(ar^{p+q-1} )^2= (pq)^2$

Taking square root on both sides ,we get

$ar^{p+q-1} ^2= pq$ → (p+q) th term

Therefore , the  (p+q) th term is pq.

# Learn more :

In a gp pth term is q and qth term is p find the (p+q)th term

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