Question
The coefficients of three consecutive terms of (1+x)n+5 are in the ratio 5 : 10 : 14. Then, n is equal to
Answer: Option D
:
D
Let the three consecutive terms in (1+x)n+5 be tr,tr+1,tr+2 having coefficients
n+5Cr−1,n+5Cr,n+5Cr+1
Given,
n+5Cr−1,n+5Cr,n+5Cr+1=5:10:14
∴n+5Crn+5Cr−1=105andn+5Cr+1n+5Cr=1410⇒n+5−(r−1)r=2andn−r+5r+1=75
⇒ n – r + 6 = 2r and 5n – 5r + 25 = 7r + 7
⇒ n + 6 = 3r and 5n + 18 = 12r
∴n+63=5n+1812
⇒ 4n + 24 = 5n + 18
⇒ n = 6
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:
D
Let the three consecutive terms in (1+x)n+5 be tr,tr+1,tr+2 having coefficients
n+5Cr−1,n+5Cr,n+5Cr+1
Given,
n+5Cr−1,n+5Cr,n+5Cr+1=5:10:14
∴n+5Crn+5Cr−1=105andn+5Cr+1n+5Cr=1410⇒n+5−(r−1)r=2andn−r+5r+1=75
⇒ n – r + 6 = 2r and 5n – 5r + 25 = 7r + 7
⇒ n + 6 = 3r and 5n + 18 = 12r
∴n+63=5n+1812
⇒ 4n + 24 = 5n + 18
⇒ n = 6
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