What will come in place of the question mark (?) in the given series? 12 17 22…

Concept

A number series built on a constant arithmetic difference adds (or subtracts) the SAME fixed value to each term to get the next one - this fixed value is called the common difference of the series.

Application

1. Find the gap between each pair of consecutive given terms: 17-12, 22-17, 27-22, and 32-27.

2. Each of these gaps works out to the SAME value, confirming the series has one constant common difference throughout.

3. Extend the series by adding that same constant difference to the last given term, 32, to get the missing term.

Cross-check

Cross-check with the nth-term rule for such a series, T(n) = T(1) + (n-1) x d, using the first term T(1)=12 and the constant difference d found above. Substituting n=6 reproduces the same value obtained by direct addition, confirming the answer.

So the term that replaces the question mark is 37.