JEE Mains · Maths · STD 11 - 7. binomial theoram
If the coefficients of the three consecutive terms in the expansion of \((1+ x )^{ n }\) are in the ratio \(1: 5: 20\), then the coefficient of the fourth term is \(............\).
- A \(3654\)
- B \(1827\)
- C \(5481\)
- D \(2436\)
Answer & Solution
Correct Answer
(A) \(3654\)
Step-by-step Solution
Detailed explanation
\(\frac{{ }^n C_r}{{ }^n C_{r-1}}=5 \quad \frac{{ }^n C_{r+1}}{{ }^n C_r}=4\) \(\frac{ n - r +1}{ r }=5 \quad n =5 r +4 \ldots(2)\) \(n=6 r-1 \ldots(1)\) \(\therefore n=29, r=5\) \(\text { Coeff of } 4^{\text {th }} \text { term }={ }^{29} C _3\) \(=3654\)
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