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# Lecture - 15 Chapter 9 Sequences & Series

MISCELLANEOUS EXERCISE |

**Example 21. **If *p*^{th}, *q*^{th}, *r*^{th} and *s*^{th} terms of an A.P. are in G.P, then show that \((p-q), (q-r), (r-s)\) are also in G.P.

**Example 22.** If *a*, *b*, *c* are in G.P. and \(a^{\frac{1}{x}}=b^{\frac{1}{y}}=c^{\frac{1}{z}}\), prove that *x*, *y*, *z* are in A.P.

**Example 23.** If *a*, *b*, *c*, *d* and *p* are different real numbers such that \((a^2+b^2+c^2)p^2-2(ab+bc+cd)p+(b^2+c^2+d^2) le 0\), then show that *a*, *b*, *c* and *d* are in G.P.

**Example 24.** If *p*, *q*, *r* are in G.P. and the equations, \(px^2+2qx+r=0\) and \(dx^2+2ex+f=0\) have a common root, then show that \(\frac{d}{p}, \frac{e}{q}, \frac{f}{r}\) are in A.P.

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