Find the next term in the series given below 5, 9, 14, 20, 27, 35, ?

Concept

In a difference pattern, compare each term with the preceding term. When consecutive differences increase by a constant amount, extend the difference sequence first and then add the next difference to the last term.

Application

1. The first difference is 9 − 5 = 4.

2. The second difference is 14 − 9 = 5.

3. The third difference is 20 − 14 = 6.

4. The fourth difference is 27 − 20 = 7.

5. The fifth difference is 35 − 27 = 8.

6. The differences 4, 5, 6, 7, 8 increase by 1, so the next difference is 9.

7. Add this difference to the last term: 35 + 9 = 44.

Cross-check

Rebuilding the sequence as 5; 5 + 4; 9 + 5; 14 + 6; 20 + 7; 27 + 8; 35 + 9 preserves the same rule at every step.

Result

Therefore, the next term is 44.