AP recognition: 1, 8, 15, … (constant difference 7) Find the 11th term.

Introduction / Context:The sequence increases by 7 each time, a classic AP scenario solvable by the nth-term formula.

Given Data / Assumptions:

• a_1 = 1, d = 7.
• Find a_11.

Concept / Approach:Use a_n = a_1 + (n−1)d.

Step-by-Step Solution:a_11 = 1 + 10*7 = 71.

Verification / Alternative check:Compute a_6 = 36; five more steps of +7 yield 71 at the 11th term.

Why Other Options Are Wrong:69, 72, 73 are close but do not match the exact +7 progression to the 11th term.

Common Pitfalls:Adding 7 eleven times instead of ten (since the first term already counts as n=1).

Final Answer:71