Sequences & Series
4-term AP — Product Condition, Largest Term
nta_pyq_2026_jan
Grade Class 11
Question:
Let $a_1,a_2,a_3,a_4$ be an A.P. of four terms such that each term of the A.P. and its common difference $l$ are integers. If $a_1+a_2+a_3+a_4=48$ and $a_1a_2a_3a_4+l^4=361$, then the largest term of the A.P. is equal to
Step-by-Step Solution
Key Concept: Let centre $=12$ (sum$=4\times12=48$). Symmetric form: $a_1=12-3l/2,a_2=12-l/2,a_3=12+l/2,a_4=12+3l/2$. Product $+l^4=361=19^2$.
$l=10$. Largest term $=27$.
<div class="key-concept"><strong>Key Concept:</strong> Let centre $=12$ (sum$=4\times12=48$). Symmetric form: $a_1=12-3l/2,a_2=12-l/2,a_3=12+l/2,a_4=12+3l/2$. Product $+l^4=361=19^2$.</div>
<div class="trap-box"><strong>Trap:</strong> Try $l=10$: $a_1=-3,a_2=7,a_3=17,a_4=27$. Product $=-3\times7\times17\times27=-9639$. $-9639+10000=361$. ✓ Largest term $=27$.</div>
Correct Answer: 3