JEE Mains · Maths · STD 11 - 8. sequence and series
Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its \(11^{\text {th }}\) term is :
- A 90
- B 84
- C 122
- D 108
Answer & Solution
Correct Answer
(A) 90
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{S}_3=3 \mathrm{a}+3 \mathrm{~d}=54 \\ & \Rightarrow \mathrm{a}+\mathrm{d}=18 \\ & \mathrm{~S}_{20}=10(2 \mathrm{a}+19 \mathrm{~d}) \\ & \Rightarrow 10(36+17 \mathrm{~d}) \\ & \Rightarrow 1600 < 10(36+17 \mathrm{~d}) < 1800 \\ & \Rightarrow 160 < 36+17…
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