# Key Points

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1.Â In AP, a_{m+n} + a_{m}_{-}_{n} = 2 a_{m}

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2.Â In AP, a_{m} = n, a_{n} = m then a_{p} = m + n â€“ p

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3.Â In AP, S_{p} = a, S_{q} = b, S_{r} = c, then

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4.Â In AP, a_{p}=a, a_{q} = b, a_{r} = c, then a (qâ€“r) + b (râ€“p) + c (pâ€“q) = 0

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5.Â If A and G be A.M and G.M., respectively between two positive numbers *x* and y then

*x* =

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6.Â If a, b, c and d are in G.P., show that (a^{2}+b^{2}+c^{2}) (b^{2}+c^{2}+d^{2}) = (ab+bc+cd)^{2}

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7.Â If p^{th}, q^{th}, r^{th} and s^{th} terms of an A.P. are in G.P. then (pâ€“q), (qâ€“r), (pâ€“q), (qâ€“r), (râ€“s) are also in G.P.

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8.Â If a, b, c are in G.P and , then *x*, y, z are in A.P.

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9.Â The ratio of the A.M and G.M. of two positive numbers a and b is m : n then

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a : b =

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10.Â Â Â Â Â Â In A.P., S_{m} = n, S_{n} = m, then S_{m+n} = â€“ (m+n)

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11.Â Â Â Â Â Â In A.P., S_{m} =

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12.Â Â Â Â Â Â In A.P., a_{m} =

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