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If 2nd, 3rd and 4th terms in the expansion of (x+a)n are 240, 720 and 1080 respectively, then the value of n is
- a)15
- b)20
- c)5
- d)10
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If 2nd, 3rd and 4th terms in the expansion of(x+a)n are 240, 720 and 1...
General term Tr+1 of (x+y)n is given by
Tr+1 = nCr xn-r yr
T2 = nC2 xn-2 y = 240
T3 = nC3 xn-3 y2 = 720
T4 = nC4 xn-4 y3 = 1080
T3/T2 = [(n-1)/2] * [y/x] = 3......(1)
T4/T2 = {[(n-1)(n-2)]/(3*2)} * x2/y2 = 9/2
T4/T3 = [(n-2)/3] * [y/x] = 3/2...(2)
Dividing 1 by 2
[(n-1)/2] * [3/(n-2)] = 2
⇒ 3n−3 = 4n−8
⇒ 5 = n
Tr+1 = nCr xn-r yr
T2 = nC2 xn-2 y = 240
T3 = nC3 xn-3 y2 = 720
T4 = nC4 xn-4 y3 = 1080
T3/T2 = [(n-1)/2] * [y/x] = 3......(1)
T4/T2 = {[(n-1)(n-2)]/(3*2)} * x2/y2 = 9/2
T4/T3 = [(n-2)/3] * [y/x] = 3/2...(2)
Dividing 1 by 2
[(n-1)/2] * [3/(n-2)] = 2
⇒ 3n−3 = 4n−8
⇒ 5 = n
Most Upvoted Answer
If 2nd, 3rd and 4th terms in the expansion of(x+a)n are 240, 720 and 1...
Given Information:
- 2nd term: 240
- 3rd term: 720
- 4th term: 1080
Solution:
Let's consider the expansion of (x + a)^n.
General Form:
The general form of the expansion of (x + a)^n is given by:
(x + a)^n = C(0)*x^n*a^0 + C(1)*x^(n-1)*a^1 + C(2)*x^(n-2)*a^2 + ... + C(n)*x^0*a^n
Given Terms:
- 2nd term: C(1)*x^(n-1)*a^1 = 240
- 3rd term: C(2)*x^(n-2)*a^2 = 720
- 4th term: C(3)*x^(n-3)*a^3 = 1080
Calculation:
From the given information, we can see that the 2nd term corresponds to C(1), the 3rd term corresponds to C(2), and the 4th term corresponds to C(3).
Therefore, n - 1 = 1 (for the 2nd term)
n - 2 = 2 (for the 3rd term)
n - 3 = 3 (for the 4th term)
Solving these equations, we get:
n = 2 + 1 = 3
Hence, the value of n is 3, which corresponds to option 'C'.
- 2nd term: 240
- 3rd term: 720
- 4th term: 1080
Solution:
Let's consider the expansion of (x + a)^n.
General Form:
The general form of the expansion of (x + a)^n is given by:
(x + a)^n = C(0)*x^n*a^0 + C(1)*x^(n-1)*a^1 + C(2)*x^(n-2)*a^2 + ... + C(n)*x^0*a^n
Given Terms:
- 2nd term: C(1)*x^(n-1)*a^1 = 240
- 3rd term: C(2)*x^(n-2)*a^2 = 720
- 4th term: C(3)*x^(n-3)*a^3 = 1080
Calculation:
From the given information, we can see that the 2nd term corresponds to C(1), the 3rd term corresponds to C(2), and the 4th term corresponds to C(3).
Therefore, n - 1 = 1 (for the 2nd term)
n - 2 = 2 (for the 3rd term)
n - 3 = 3 (for the 4th term)
Solving these equations, we get:
n = 2 + 1 = 3
Hence, the value of n is 3, which corresponds to option 'C'.
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