Question
If $a, b, c, d$ are in GP, then $(b+c)^{2}=$ _______.(1) $(b+d)(a+d)$(2) $(a+d)(c+d)$(3) $(a+b)(c+d)$(4) $(a+c)(b+d)$
Step 1
Step 1: Given that $a, b, c, d$ are in geometric progression, we can write $b = ar$, $c = ar^{2}$, and $d = ar^{3}$, where $r$ is the common ratio of the geometric progression. Show more…
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If $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}$ are in GP then (a) $\mathrm{a}+\mathrm{b}, \mathrm{b}+c_{2} \mathrm{c}+\mathrm{d}$ are in $\mathrm{GP}$ (b) $a x^{2}+c$ is a factor of $a x^{3}+b x^{2}+c x+d$ (c) $a^{2}+b^{2}+c^{2}, a b+b c+c d, b^{2}+c^{2}+d^{2}$ are in GP (d) $a x+c$ is a factor of $a x^{3}+b x^{2}+c x+d$
If $a, b, c$ are in AP, $b-a, c-b$ and $a$ are in GP, then find $a: b: c$.
If $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in $\mathrm{AP}$, then $4\left(\mathrm{~b}^{2}-\mathrm{ac}\right)=$ (a) $a^{2} c+3$ (b) $\frac{\mathrm{a}+\mathrm{c}}{2}$ (c) $\frac{(a+c) a}{3}$ (d) $(\mathrm{a}-\mathrm{c})^{2}$
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