The fixed number is called the common difference of the progression <strong>and</strong> is usually denoted by d. Thus in (i), common difference (d) is 1, In (ii), common difference is 2 <strong>and</strong> in (iii), common difference is 5. The first term of an arithmetic progression (<strong>AP</strong>) is usually written as a. Thus, in general, If a is the first term <strong>and</strong> d, the common difference of an <strong>AP</strong>, then the <strong>AP</strong> can be written as a, a + d, a + 2d, a+3d, …. Note that in case of an <strong>AP</strong>, it is obvious that common difference = second term – first term = third term – second term = fourth term – third term <strong>and</strong> so on. Example 4: Identify which of the following are arithmetic progressions. For those which are arithmetic progressions, find the common differences : (i) 3, 6, 12, 24,…… (ii) 12, 2, – 8, – 18,…… (iii) 0, , , , ……. (iv) , , , , .…… (v) 1, 1.7, 2.4, 3.1, ……. (vi) 1 2 , 5 2 , 7 2 , 73,……. 45
Solution: (i) 3, 6, 12, 24,… We see that 6 3 = 3 12 6 = 6 24 12 = 12 Thus, it is not an <strong>AP</strong>. [As 3 6 12] (ii) 12, 2, 8, -18,……. Here, 2 12 = <strong>10</strong> 8 2 = <strong>10</strong> 18 (– 8) = 18 + 8 = <strong>10</strong> Thus, it is an <strong>AP</strong>. Here, common difference (d) is <strong>10</strong> (iii) 0, , , , ….. We have 0 = – = – = Thus, it is also an <strong>AP</strong> with common difference (d) = (iv) , , , , …. We have 46
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CBSE-i Mathematics Arithmetic Progr
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Step 6 Take the strip of dimension
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PCW4 Framing questions Using the gi
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Suggested videos and Extra readings