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| Arithmetic Progression (or simply A.P.) |
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| Quantities are said to be in Arithmetic progression when they increase or decrease by a common difference. |
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| Examples: |
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| Each one of the following series form an A.P. |
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| i) 1, 3, 5, 7, … |
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| ii) 3, 7, 11, 15, … |
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| iii) 15, 12, 9, … |
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| iv) x, x - d, x - 2d, ..... |
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| The common difference is found by subtracting any term of the series from the immediate succeeding term. |
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| In the above example, common difference in the first is 2, in the second it is 4, in the third it is -3, in the fourth it is -d and in the fifth it is d. |
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| The general form of an A.P. is as follows: |
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| a = first term, d = common difference, then A.P. is a, a+d, a+2d, a+3d,..... |
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| We observe that in any term the coefficient of d is always less by one than the number of terms in the series. |
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| Thus, second term is a+d |
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| third term is a+2d |
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| fourth term is a+3d |
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| tenth term is a+9d |
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| and generally, nth term is a + (n-1)d. |
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| If n is the number of terms and if tn is the nth term, then tn = a+(n-1)d. |
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| To find the sum of a number of terms in Arithmetical Progression: |
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| Let a=first term, d=common difference, l=tn=last term, s=required
sum. Then, |
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| Writing the series in the reverse order, |
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| Adding together the two series, |
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