Find the next two terms in the series: 9 16 23 30 37 44 51

Concept: In an arithmetic (addition) number series, consecutive terms differ by a constant common difference d; once d is found from any two consecutive given terms, every later term equals the previous term plus d.

Application:

1. Find the difference between each pair of consecutive given terms: 16-9=7, 23-16=7, 30-23=7, 37-30=7, 44-37=7, 51-44=7.

2. Every difference equals 7, so the common difference d=7 for this series.

3. Add d to the last given term: 51+7=58, giving the eighth term.

4. Add d again to get the ninth term: 58+7=65.

Cross-check: Using the general term a(n) = 9 + (n-1)×7, the 8th term a(8) = 9 + 7×7 = 58 and the 9th term a(9) = 9 + 8×7 = 65 — the same pair, 58 and 65.