Find the missing number in the following series: 2, 3, 5, 8, 13, ?, 34

Concept: In an additive (Fibonacci-type) number series, every term from the third term onward equals the sum of the two terms immediately before it — that is, if the terms are T1, T2, T3, … , then Tn = Tn−1 + Tn−2 for n ≥ 3.

Application:

1. Label the given terms by position: T1=2, T2=3, T3=5, T4=8, T5=13, T6=?, T7=34.

2. Confirm the additive rule already holds for the given terms: T3 = T2 + T1 = 3 + 2 = 5; T4 = T3 + T2 = 5 + 3 = 8; T5 = T4 + T3 = 8 + 5 = 13.

3. Apply the same rule to find the missing term: T6 = T5 + T4 = 13 + 8 = 21.

Cross-check: take the rule one step further using the newly found term — T7 = T6 + T5 = 21 + 13 = 34, which matches the last term given in the series, confirming the pattern holds throughout.

Therefore, the missing number is 21.