Complete the sequence: 5939, 5932,
5925, what, what, what, and what?
All the whats as we read the
question show that there are four missing numbers to this sequence. And the question is asking us to
find them to complete the sequence. To do this, we need to look at the
three numbers that we’ve been given already and try and work out what the rule for
the sequence is. Our numbers are 5939, 5932, and
5925. What do we notice about these
Well, the first thing we can say
about the sequence is that it’s a decreasing pattern. As we go from one number to the
other, the numbers are getting less and less. But by how much? Our first number has five
thousands, nine hundreds, three tens, and nine ones. Our second number has five
thousands, nine hundreds, three tens, and two ones. The number of thousands has stayed
the same, as has the number of hundreds and also the number of tens.
In fact, the only part of the
number that’s changed is the ones. We’ve gone from nine ones to two
ones. How do we get from nine to two? Well, we know that two and seven
make nine. So nine take away seven will leave
us with two. Let’s see whether subtracting seven
is the rule for the pattern. We’ll have a look at the next
We have five thousands, nine
hundreds. This time, the tens digit has
changed and the ones digit. If we look at the number we were
starting from, it ended in 32. And 32 take away seven does equal
25. The next number in the sequence
will be 5925.
Now that we know what the rule for
the sequence is, we can find our remaining four numbers. We know that 25 take away seven
equals 18. And so 5925 take away seven will be
5918. 5918 has eight ones. So we can subtract seven
quickly. Eight take away seven equals
one. So the next number in our sequence
is 5911. Seven plus four equals 11. So if we take away seven from 5911,
we’re left with 5904.
Finally, we can split the seven
that we want to subtract into four and three. If we take away four from 5904,
we’re left with 5900. Now if we take away the remaining
three, we’re left with 5897.
We’ve found that our sequence was a
decreasing one and that the rule was to take away seven each time. The completed sequence is 5939,
5932, 5925, and then our four missing numbers, 5918, 5911, 5904, and 5897.