Mathematics
The 10th, 16th and 22nd terms of a G.P. are x, y and z respectively. Show that x, y and z are in G.P.
AP GP
25 Likes
Answer
Let first term of G.P. be a and common ratio be r.
By formula,
⇒ an = arn - 1
Given,
The 10th, 16th and 22nd terms of a G.P. are x, y and z respectively.
⇒ a10 = x
⇒ x = ar10 - 1
⇒ x = ar9 ………..(1)
⇒ a16 = y
⇒ y = ar16 - 1
⇒ y = ar15 ………..(2)
⇒ a22 = z
⇒ z = ar22 - 1
⇒ z = ar21 ………..(3)
Dividing equation (2) by (1), we get :
Dividing equation (3) by (2), we get :
Since, = r6.
Hence, proved that x, y and z are in G.P.
Answered By
12 Likes