Question

If p Q r are in a AP then, pth, qth, rth terms of any gp are themselves in
​

Answer 1

Step-by-step explanation:

p, q and r are in A.P

i.e. 2q=p+r

General term of G.P is T(K)=ar

(k−1)

p

th

term is :- T(p)=ar

(p−1)

...(1)

q

th

term is :- T(q)=ar

(q−1)

...(2)

r

th

term is :- T(r)=ar

(R−1)

...(3)

To prove that ;- T(p),T(q),T(r) are in G.P

T(q)

2

=T(p).T(r)

[ar

(q−1)

]

2

=ar

(p−1)

.ar

(R−1)

a

2

ar

2(q−1)

=a

2

r

(p−1)

r

(R−1)

r

2(q−1)

=r

(P+R−2)

Taking only powers

2(q−1)=P+R−2

2q−2=P+R−2

2q=P+R

This proves that p

th

,q

th

and r

th

term are in G.P

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