[數學] 數學問題

Here are the first five terms of a number sequence.

1,4,16,64,256,

Question:

The 5th term, 256, of the sequence ends with the number 6

What number does the 29th term of the sequence end with ?

標準答案是: 6

本人想知道答案是怎樣計算出來? 為何是6?

Thanks

2 Answers

Rating
  • 8 years ago
    Favorite Answer

    From above, we can see this is a geometric sequence with a common ratio which is 4.

    4 x 4 = 16

    6 x 4 = 24

    44 x 4 = 176

    44 x 6 = 264

    From the above examples, we can note that whenever 4 x 4, the last digit of the answer must be 6, while 6 x 4, the last digit of the answer must be 4.

    For instance, if we expand the sequence, we can see 1,4,16,64,256,1024,,4096...

    The last digits of the answers(apart from the first one), goes with 4, 6, 4, 6....

    As we can see, for all the odd terms of the sequence (apart form the first one), all ends with 6.

    Therefore, for the last digit of the 29th of the sequence is also 6.

  • 8 years ago

    1,4,16,64,256

    這是4的n次方數列﹐由觀察可知當n是奇數時﹐個位數是6;當n是偶數時﹐個位數是4

    而29是奇數﹐因此第29項的個位數是6

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