WORKED EXAMPLE · 4 MIN READ

A sequence, explained with two rows of differences

Solve 2, 5, 10, 17, 26 by checking the differences, then test why plausible alternative choices do not fit.

PulsePuzzle · Reviewed October 13, 2026

A number sequence can look irregular until you write down how much each term changes. This practice example shows how a simple second row turns an uncertain guess into an explanation you can check. It is a teaching example rather than today's NumberPulse puzzle.

The problem

The displayed sequence is 2, 5, 10, 17, 26, ?. The four answer options are 35, 36, 37, and 39. Before choosing, predict a rule that explains all five visible terms.

Calculate neighboring differences

The differences are not constant, so “add the same amount” does not explain the sequence. But they form another row: 3, 5, 7, 9. Each difference increases by two. Continuing that pattern gives a next difference of 11.

Return to the original row

The missing term is not 11; that is the next change. Add it to the last visible term: 26 + 11 = 37. This distinction matters whenever you create a differences row. Keep track of which row your prediction belongs to before matching it to an option.

You can describe the same sequence another way. The terms are one more than consecutive squares: 1² + 1 = 2, 2² + 1 = 5, through 5² + 1 = 26. The next is 6² + 1 = 37. This is a useful cross-check rather than a separate requirement; the differences explanation already supports the choice.

Check the tempting alternatives

Choosing 35 repeats the most recent difference of 9. That ignores the fact that the preceding differences increased. Choosing 36 notices a square but forgets the extra one present in every visible term. Choosing 39 gives a jump of 13, skipping the 11 that would continue the differences row.

These rejections are about this intended pattern. A finite sequence permits other extensions, including contrived formulas. The useful task is to find a consistent, economical description of the evidence shown, then test that description against every visible transition.

Try the method on another row

Find the next value in 1, 4, 9, 16, ?. Write the differences and predict the next difference before adding it.

NumberPulse has one sequence each day and adds five seconds for a wrong choice. Read the NumberPulse guide for other checks, including ratios and alternating rows, or try today's sequence.