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| Arithmetic Mean (A.M.) |
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| 1. If a, x, b are in A.P, then x is called the arithmetic mean (A.M.) between the extremes a and b. |
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| 2. a. To insert n arithmetic means between two given quantities. |
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| Let a and b be any two given quantities,
and let A1,A2,A3,-----An be n arithmetic means to be inserted between a and b so that
a, A1,A2,A3,-----An, b will be
in A.P. |
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| Let d be the common difference. |
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| Now the total number of terms including a and b is (n+2) |
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| - - - - - |
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| Hence the n arithmetic means are: |
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| These can be inserted between a and b. |
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| b. To find the sum of n arithmetic means between the two given quantities: |
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| Let the two quantities (numbers) be a and b. |
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| The required sum = A1 + A2 + A3 + ---- + An |
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