WBJEE · Maths · Sequences and Series
The sum of the first four terms of an arithmetic progression is 56 . The sum of the last four terms is 112 . If its first term is 11 , then the number of terms is
- A \(10\)
- B \(11\)
- C \(12\)
- D \(13\)
Answer & Solution
Correct Answer
(B) \(11\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & a+a+d+a+2 d+a+3 d=56 \\ & 4 a+6 d=56 \\ & 6 d=56-44=12 \\ & \Rightarrow d=2 \\ & t_1+t_2+t_3+t_4=56 \\ & t_{n-3}+t_{n-2}+t_{n-1}+t_n=112 \\ & t_1=11 \\ & t_1+t_n=t_2+t_{n-1}=t_3+t_{n-2}=t_4+t_{n-3}=k \\ & t_1+t_2+t_3+t_4+t_n+t_{n-1}+t_{n-2}+t_{n-3}=4 k \\ &…
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