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Find the two successive terms in the exp...

Find the two successive terms in the expansion of `(1+x)^(24)` whose coefficients are in the ratio `1 : 4`.

A

3rd and 4th

B

4th and 5th

C

5th and 6th

D

6th and 7th

Text Solution

Verified by Experts

The correct Answer is:
C
Let two successive terms in the expansion of `(1 + x)^(24) " are " (r + 1) th " and " (r + 2)th` terms.
`:. T_(r + 1) = .^(24)C_(r) x'`
and `T_(r + 2) = .^(24)C_(r + 1) x^(r + 1)`
given that, `(.^(24)C_(r))/(.^(24)C_(r + 1)) = (1)/(4)`
`rArr (((24)!)/(r! (24 - r)!))/(((24)!)/((r + 1) ! (24 0 r - 1)!)) = (1)/(4)`
`rArr ((r + 1) r! (23 - r)!)/(r! (24 - r) (23 - r)!) = (1)/(4)`
`rArr (r + 1)/(24 - r) = (1)/(4) rArr 4 r + 4 = 24 - r`
`rArr 5 r = 20 rArr r = 4`
`:. T_(4 + 1) = T_(5) " and " T_(4 + 2) = T_(6)`
Hence, 5th and 6th terms.
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