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STEP II 1997 question 1 solution
From The Student RoomTSR Wiki > Study Help > Subjects and Revision > Mathematics > STEP > STEP II 1997 question 1 solution Note that the first term + last term, 2000+5777 = 7777. The second term + last-1'th term, 2002+5775 = 7777, and so on. We only have to consider the number of terms in the 2000's and 5000's. As we are adding the terms up, we need to find the number of terms in the 2000's. Looking at the progression: 2000 2002 2005 2007
2020 2022 2025 2027
2050 2052 2055 2057
2070 2072 2075 2077 etc... There are 16 terms with the first two digits, and this occurs 4 times with each different hundreds number, so there are 64 "sets" of 7777. Therefore:
Done. Solution by Lusus Naturae |
