Crack the Sequence Code

Some number sequences look like secret codes. But one tiny gap can unlock every missing number... if you know where to look. The numbers can climb, fall, or cross a hundred.

A sequence is an ordered line of numbers. To find its rule, compare one term with the NEXT term. Ask: what single addition or subtraction changes the first whole number into the second? Each gap must use exactly the same rule. Here are forty-two, forty-seven, fifty-two and fifty-seven. Forty-two to forty-seven is add five. Check again: forty-seven plus five is fifty-two. The same jump works twice, so the rule is add five. Matching arrows appear beneath both gaps, each showing plus five. Now the row continues to an empty box. Apply the rule once more: fifty-seven plus five makes sixty-two. The next term is sixty-two. A curved arrow labelled plus five lands on it. Watch out: compare the WHOLE numbers, not only their final digits. From fifty-seven to sixty-two, seven becomes two, but the number has increased by five. Always test your rule on at least two gaps.

Let's work through an example. A number sequence begins one hundred and forty-seven, one hundred and thirty-five, one hundred and twenty-three, one hundred and eleven. What are the next two terms? Write both answers in the boxes. First, find the change between neighbouring terms. One hundred and forty-seven minus twelve equals one hundred and thirty-five. So the first gap is subtract twelve. A downward arrow shows that jump beneath the first pair. Do not rush ahead yet. Test the same rule: one hundred and thirty-five minus twelve equals one hundred and twenty-three. It works again. The rule is SUBTRACT twelve each time. Now continue carefully. One hundred and eleven minus twelve equals ninety-nine, so the first missing term is ninety-nine. Ninety-nine minus twelve equals eighty-seven, so the second missing term is eighty-seven. Two amber ticks confirm that both completed gaps match.

Find one gap, check another, then repeat the same rule. You can crack an arithmetic sequence with confidence!