If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

Asked by Pragya Singh | 1 year ago |  77

##### Solution :-

Let a be the first term and r be the common ratio of the G.P.

According to the given condition,

a4 = a r3 = x … (1)

a10 = a r9 = y … (2)

a16 = a r15 = z … (3)

On dividing (2) by (1), we get

$$\dfrac{y}{x}= \dfrac{ar^9}{ar^3}$$

$$\dfrac{y}{x}=r^6$$

Now, divide equation (3) by (2).

$$\dfrac{z}{y}= \dfrac{ar^{15}}{ar^9}$$

$$\dfrac{z}{y}= r^6$$

$$\dfrac{y}{x}= \dfrac{z}{y}$$

Therefore, it is proved that x, y, z are in G. P.

Answered by Abhisek | 1 year ago

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