40 a If the sum of the whole numbers from 1 B1 2 B1 for clear explanation. M to 50 is 1275 the sum from 2 to 51 will be 1275 + 51 1 = 1325. – b Check method, using simple examples. B1 B1 for clear explanation Sn c Using = B2 B1 for clear use of the formula S52 == 1326 B1 for showing same answer as above 1326 1 + 1325 as above. – nth If 1 is the first term then the term d n, n. will be so their sum is 1 + B2 B1 for clear explanation. Because they come in pairs, there will B1 for use of the generalization and good mathematical be of these pairs adding to the total. language. So the total = (n + 1) × =, the formula given. 6
40 a b c d If the sum of the whole numbers from 1 to 50 is 1275 the sum from 2 to 51 will be 1275 + 51 – 1 = 1325. Check method, using simple examples. Using Sn = S52 == 1326 1326 – 1 + 1325 as above. If 1 is the first term then the nth term will be n, so their sum is 1 + n. Because they come in pairs, there will be of these pairs adding to the total. So the total = (n + 1) × =, the formula given. B1 B1 B2 B2 2 B1 for clear explanation. B1 for clear explanation B1 for clear use of the formula B1 for showing same answer as above B1 for clear explanation. B1 for use of the generalization and good mathematical language. M 6
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