Arithmetic progression (AP): 3, 9, 15, 21, … Find the 15th term of the AP.

Introduction / Context:
In an AP, each term increases by a fixed common difference d. The nth term formula a_n = a_1 + (n−1)d gives any target term directly.

Given Data / Assumptions:

• a_1 = 3, d = 6 (since 9−3 = 6).
• We seek a_15.

Concept / Approach:
Apply the nth-term formula: a_n = a_1 + (n−1)d. Substitute n = 15 with the known a_1 and d.

Step-by-Step Solution:
a_15 = 3 + (15−1)*6 = 3 + 14*6 = 3 + 84 = 87.

Verification / Alternative check:
List a few terms or compute a_10 = 3 + 9*6 = 57 and add five more differences (5*6 = 30) to reach 87.

Why Other Options Are Wrong:
80 and 85 undercount the added differences; 90 overshoots by one extra step.

Common Pitfalls:
Using n*d instead of (n−1)d; miscounting from the first term.

Final Answer:
87