The 10 th , 16 th and 22 nd terms of a G.P. are x, y and z respectively. Show that x, y and z are in G.P.

Let first term of G.P. be a and common ratio be r. By formula, ⇒ a n = ar n - 1 Given, The 10 th , 16 th and 22 nd terms of a G.P. are x, y and z respectively. ⇒ a 10 = x ⇒ x = ar 10 - 1 ⇒ x = ar 9 ...........(1) ⇒ a 16 = y ⇒ y = ar 16 - 1 ⇒ y = ar 15 ...........(2) ⇒ a 22 = z ⇒ z = ar 22 - 1 ⇒ z = ar 21 ...........(3) Dividing equation (2) by (1), we get : Dividing equation (3) by (2), we get : Since, = r 6 . Hence, proved that x, y and z are in G.P.

Find the 8^th term of a G.P., if its common ratio is 2 and 10^th term is 768.

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x, 2x + 2, 3x + 3, G are four consecutive terms of a G.P. Find the value of G.

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The third term of a G.P. is 2. Find the product of the first five terms of this G.P.

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Mathematics

The 10^th, 16^th and 22^nd terms of a G.P. are x, y and z respectively. Show that x, y and z are in G.P.

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Related Questions

Find the 8^th term of a G.P., if its common ratio is 2 and 10^th term is 768.

x, 2x + 2, 3x + 3, G are four consecutive terms of a G.P. Find the value of G.

The third term of a G.P. is 2. Find the product of the first five terms of this G.P.

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

Related Questions

Find the 8th term of a G.P., if its common ratio is 2 and 10th term is 768.

x, 2x + 2, 3x + 3, G are four consecutive terms of a G.P. Find the value of G.

The third term of a G.P. is 2. Find the product of the first five terms of this G.P.

The 10^th, 16^th and 22^nd terms of a G.P. are x, y and z respectively. Show that x, y and z are in G.P.

Find the 8^th term of a G.P., if its common ratio is 2 and 10^th term is 768.