AP identification: 10, 8, 6, 4, … What term of this AP is −28?

Introduction / Context:
Solving “which term equals a specific value” in an AP means solving a linear equation in n using the nth-term form.

Given Data / Assumptions:

• a_1 = 10, d = −2.
• Find n such that a_n = −28.

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

Step-by-Step Solution:
a_n = 10 + (n−1)(−2) = 10 − 2n + 2 = 12 − 2n.Set 12 − 2n = −28 ⇒ −2n = −40 ⇒ n = 20.

Verification / Alternative check:
Compute a_20 directly: 10 + 19*(−2) = 10 − 38 = −28 (confirms).

Why Other Options Are Wrong:
15, 18, 19 correspond to intermediate terms whose values are −18, −24, −26 respectively, not −28.

Common Pitfalls:
Algebraic slip when distributing the negative sign or using n instead of (n−1).

Final Answer:
20