Question
If a, b, c, d are in G.P., prove that:
$(\text{b}+\text{c})(\text{b}+\text{d})=(\text{c}+\text{a})(\text{c}+\text{d})$
$(\text{b}+\text{c})(\text{b}+\text{d})=(\text{c}+\text{a})(\text{c}+\text{d})$
$\therefore\text{b}^2=\text{ac }\cdots(1)$
$\text{L.H.S}=({\text{b}+\text{a})(\text{b}+\text{d})}$ $=\text{b}^2+\text{bd}+\text{bc}+\text{cd}$ $=\text{ac}+\text{c}^2+\text{ad}+\text{cd}$ $[\text{Using (1)}]$ $=\text{c}(\text{a}+\text{c})+\text{d}(\text{a}+\text{c})$ $=(\text{c}+\text{a})(\text{c}+\text{d})$ $=\text{R.H.S}$$\therefore\text{R.H.S}=\text{L.H.S}$
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If the 2nd, 3rd and 4th terms in the expansion of $(\text{x}+\text{a})^{\text{n}}$ are 240, 729 and 1080 respectively
find x, a, n.| xi | 10 | 30 | 50 | 70 | 90 |
| fi | 4 | 24 | 28 | 16 | 8 |