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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.