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Point Slope Form of a Line

37. Line A1 a...

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37. Line A1 and A2 intersect at point (-2.1) making an angle of pi/6 with each other. If the slope of A2 is 1/2, then find equation of A1.

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a_{1}, a_{2}, a_{3} \dots, a_{n}

are in AP, where

a_{i} > 0

for all i, then the value of

\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + \dots + \frac{1}{\sqrt{a_{n - 2}} + \sqrt{a_{n}}}

a_{1}, a_{2}, a_{3}, . . . . . a_{n}

are in H.P., then

\frac{a_{1}}{a_{2} + a_{3} + . . . a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . . + a_{n}}, \frac{a_{n}}{a_{1} + a_{2} + . . . + a_{n - 1}}

a_{1}, a_{2}, a_{3}, . . . . a_{n}

are in H.P, then

\frac{a_{1}}{a_{2} + a_{3} + . . . . + a_{n}}, \frac{a_{2}}{a_{1} + a_{3} + . . . . + a_{n}}, . . . ., \frac{a_{n}}{a_{1} + a_{2} + . . . . + a_{n - 1}}

a_{1}, a_{2}, a_{3}, . . . . . . . a_{n}

are in A.P. where

a_{1} > 0

\forall

\frac{1}{\sqrt{a_{1}} + \sqrt{a_{2}}} + \frac{1}{\sqrt{a_{2}} + \sqrt{a_{3}}} + . . . . . + \frac{1}{\sqrt{a_{n - 1}} + \sqrt{a_{n}}} = \frac{k}{\sqrt{a_{1}} + \sqrt{a_{n}}}

k

\frac{a_{1}}{a_{1}} + \frac{a_{2}}{a_{2}} + \frac{a_{3}}{a_{3}} + \dots \frac{a_{n}}{a_{n}} = \frac{1}{1} + \frac{1}{a_{1}} + \frac{a_{1}}{a_{2}} + \frac{a_{2}}{a_{3}} + \dots \frac{a_{n - 2}}{a_{n - 1}}

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