Question

If p,q,r,s are in G.P show that p+q,q+r,r+s are also in G.P..​

Answer 1

If p,q,r,s are in G.P show that p+q,q+r,r+s are also in G.P

p, q , r , s are in GP.

we know, the standard form of geometric progression is ; a, ar, ar², ar³, ....

let p = a, q = ar, r = ar² and s = ar³

now, p + q = a + ar = a(1 + r)

q + r = ar + ar² = ar(1 + r)

r + s = ar² + ar³ = ar²(1 + r)

now tell me , a(1 + r), ar(1 + r), ar²(1 + r) is in GP ? of course yes !

because common ratio of two successive terms always remains same.

i.e., {ar(1 + r)}/a(1 + r) = {ar²(1 + r)}/{ar(1 + r)} = r

so, (p + q), (q + r), (r + s) are also in GP. hence, proved .

Answer 2

Answer:

Step-by-step explanation: