JEE Mathematics 2026 Question with Solution

Given: $a_1,a_2,a_3,a_4$ are four terms in A.P., all terms and the common difference are integers. Also,

and

Find: The largest term of the A.P.

From the solution, take the general A.P. terms as

Using the sum condition,

so

Using the product condition shown in the solution,

therefore

The solution then states an intermediate trial

which gives

but it immediately revises this and says that checking the full condition yields the valid sequence

and then concludes largest term = $27$.

There is an internal discrepancy in the extracted solution working, because the displayed sequence $12,15,18,21$ has largest term $21$, while the page marks Option A as correct and concludes $27$. Following the solution authority for the marked answer, the correct option is A.

Given: The page marks Option A as correct. Find: Which option should be recorded from the extracted page content.

The extracted working contains conflicting statements:

1. It gets $a=6, d=5$, which gives largest term $21$.
2. It then writes the sequence $12,15,18,21$, whose largest term is also $21$.
3. Despite that, it concludes largest term $27$ and marks Option A.

Since the source solution explicitly states The Correct Option is A, and answer resolution prioritizes the solution over the answer key, the recorded answer is A, while preserving the inconsistency in the explanation.