Arithmetic progression

Arithmetic progression

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  ARITHMETIC PROGRESSION BY KARUNESH KUMARSINGH GOVT. POLYTECHNIC RAMPUR (UP)
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  SEQUENCE  The sequenceis a set of numbers which are written in some particular order.  Example: 1,2,3,4,…  4,3,2,1,………..is the different sequence.
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  ARITHMETIC PROGRESSION  AnArithmetic Progression is a sequence of numbers such that the common difference of any two successive members is a constant.  Example 1. sequence 1,2,3,4,…. is an A.P. with common difference 1.  Example 2. sequence 3,5,7,9,11,… is an A.P. with common difference 2.
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  NOTATIONS  We denotefirst term, common difference, nth term , last term and sum of first n terms of A.P by respectively. SnlTnda ,,,,
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  GENERAL FORM OFAN A.P. ,...3,2,, dadadaa 
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  FORMULAS dnaTn )1(  )( )}1(2{ 2 2 la dnaS n n n  
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  PROPERTIES 2 11   nn n TT T The middle term of A.P. is the mean of adjacent terms.
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  QUESTIONS/ANSWERS  Find the10th term of an A.P. 1, 11, 21, 31… Ans: 9110)110(110 T
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  QUESTIONS/ANSWERS  An A.P.has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Find Common difference.  Ans: a=3, 4 3 2 5 2 8 58 68 20302824 }46{5}76{4 }])15(32{[2})18(32{ 2       d d dd dd dd SS