***NUMBER SEQUENCES*** How do YOU solve them?? Its been interesting recently, seeing ppl arrive at correct answers to a problem using very different methods. Remember that theres so often more than one right answer! What is the next number in this sequence? 16 22 34 58 106 …(?) This number sequence (above) was one of these, & I wonder how many approaches there are...? Ive described roughly how I analyse number sequences: do other ppl have a different strategy? The 1st step is: FIND THE PATTERN. i.e. the relationship(s) between the numbers already there. This is found by calculating the arithmetical difference between successive numbers: i.e. use addition/subtraction: Write down the successive differences in order. A pattern is usually easy to see. Sometimes the differences may increase &/ or decrease dramatically; indicating probable multiplying &/ or dividing of successive numbers: but you can pick out a pattern here also. If neither pattern is obvious, try other operations such as ^, √, ³√, etc. The first series of differences was: 6, 12, 24, 48, & 96. Clearly all multiples of 6; but each time by a different multiple. Then write down how many 6s each time, i.e, a 2nd sequence of numbers of workings: 1, 2, 4, 8, 16. And thats the basis of the answer! That sequence is equivalent to: 2^0, 2^1, 2^2, 2^3, etc. (now a third number sequence!) Let the numbers in the original sequence be P1, P2, P3, etc; we have part of the formula: 6*2^(x) However that alone is insufficient, as 6*2^0 = 6; but the first number of the sequence is 16, not 6. The difference is 10, so we look at each number to see whether it is always 10 - and it is. So with that factored in, we have: 10 + 6 * (2^x) I dont really have to write the rest, do I? I think & hope its straightforward now... :-) Please leave a note if u have time, if you have different ways. Thanks. :-)
Posted on: Fri, 16 Jan 2015 23:41:43 +0000
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