if three successive coefficients in the expressions of (1+x)n are 220, 495 and 792 respectively, find the value of n?

LetTr , Tr+1 , Tr+2 be the sucessive terms in the expansionof (1+x)n Now Tp+1 in (1+x)n = nCpxp => coefficient of (p+1)th term = nCp : Coefficient of rth term = nCr-1 = 220 (1) { p+1 = r => p = r-1 } Coefficient of (r+1)th term = nCr =495 (2) { p+1 = r+1 => p = r} Coefficient of (r+2)th term = nCr+1 = 792 (3) { p+1 = r+

if three successive coefficients in the expressions of (1+x)ⁿ are 220, 495 and 792 respectively, find the value of n?

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Uday Kiran answered this

LetT_r , T_r+1 , T_r+2 be the sucessive terms in the expansionof (1+x)ⁿ

Now T_p+1 in (1+x)ⁿ = ⁿC_px^p => coefficient of (p+1)th term = ⁿC_p

. : Coefficient of rth term = ⁿC_r-1 = 220 ..........(1) { p+1 = r => p = r-1 }

Coefficient of (r+1)th term = ⁿC_r =495 ..........(2) { p+1 = r+1 => p = r}

Coefficient of (r+2)th term = ⁿC_r+1 = 792 ..........(3) { p+1 = r+

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Uday Kiran answered this

LetT_r , T_r+1 , T_r+2 be the sucessive terms in the expansionof (1+x)ⁿ

Now T_p+1 in (1+x)ⁿ = ⁿC_px^p => coefficient of (p+1)th term = ⁿC_p

. : Coefficient of rth term = ⁿC_r-1 = 220 ..........(1) { p+1 = r => p = r-1 }

Coefficient of (r+1)th term = ⁿC_r =495 ..........(2) { p+1 = r+1 => p = r}

Coefficient of (r+2)th term = ⁿC_r+1 = 792 ..........(3) { p+1 = r+2 => p = r+1 }

Dividing (2) by (1) we get

ⁿC_r/ⁿC_r-1= 495 / 220

=> n! / (n-r) ! r ! * (n-r+1) ! (r-1) ! / n !

=> n - r +1 / r = 9/4

=> 4(n - r +1) = 9r

=> 4n - 4r +4 = 9r

=> 4n +4 = 9r + 4r

=> 4n - 13r +4 = 0 ...........(4)

Dividing (3) by (2) we get

ⁿC_r+1/ⁿC_r= 792/ 495

=> n! / (n-r-1) ! (r+1) ! * (n-r) ! r ! / n ! = 8/5

=> n - r / r + 1 = 8 / 5

=> 5n - 13r -8 = 0

Subtracting (5) from (4) we get

4n - 13r +4 = 0

5n - 13r -8 = 0 &nb

Uday Kiran answered this

LetT_r , T_r+1 , T_r+2 be the sucessive terms in the expansionof (1+x)ⁿ

Now T_p+1 in (1+x)ⁿ = ⁿC_px^p => coefficient of (p+1)th term = ⁿC_p

. : Coefficient of rth term = ⁿC_r-1 = 220 ..........(1) { p+1 = r => p = r-1 }

Coefficient of (r+1)th term = ⁿC_r =495 ..........(2) { p+1 = r+1 => p = r}

Coefficient of (r+2)th term = ⁿC_r+1 = 792 ..........(3) { p+1 = r+2 => p = r+1 }

Dividing (2) by (1) we get

ⁿC_r/ⁿC_r-1= 495 / 220

=> n - r +1 / r = 9/4

=> 4(n - r +1) = 9r

=> 4n - 4r +4 = 9r

=> 4n +4 = 9r + 4r

=> 4n - 13r +4 = 0 ...........(4)

Dividing (3) by (2) we get

ⁿC_r+1/ⁿC_r= 792/ 495

=> n - r / r + 1 = 8 / 5

=> 5n - 13r -8 = 0

Subtracting (5) from (4) we get

4n - 13r +4 = 0

5n - 13r -8 = 0 %2

-1

Uday Kiran answered this

LetT_r , T_r+1 , T_r+2 be the sucessive terms in the expansionof (1+x)ⁿ

Now T_p+1

Hayate Ayasaki answered this

thank you so much @geethanjali!!!!! :)

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Inderjeet Saluja answered this

LetT_r , T_r+1 , T_r+2 be the sucessive terms in the expansionof (1+x)ⁿ

Now T_p+1 in (1+x)ⁿ = ⁿC_px^p => coefficient of (p+1)th term = ⁿC_p

. : Coefficient of rth term = ⁿC_r-1 = 220 ..........(1) { p+1 = r => p = r-1 }

Coefficient of (r+1)th term = ⁿC_r =495 ..........(2) { p+1 = r+1 => p = r}

Coefficient of (r+2)th term = ⁿC_r+1 = 792 ..........(3) { p+1 = r

P. Rahul Dev answered this

LetT_r , T_r+1 , T_r+2 be the sucessive terms in the expansionof (1+x)ⁿ

Now T_p+1 in (1+x)ⁿ = ⁿC_px^p => coefficient of (p+1)th term = ⁿC_p

. : Coefficient of rth term = ⁿC_r-1 = 220 ..........(1) { p+1 = r => p = r-1 }

Coefficient of (r+1)th term = ⁿC_r =495 ..........(2) { p+1 = r+1 => p = r}

Coefficient of (r+2)th term = ⁿC_r+1 = 792 ..........(3) { p+1 = r

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P. Rahul Dev answered this

LetT_r , T_r+1 , T_r+2 be the sucessive terms in the expansionof (1+x)ⁿ

Now T_p+1 in (1+x)ⁿ = ⁿC_px^p => coefficient of (p+1)th term = ⁿC_p

. : Coefficient of rth term = ⁿC_r-1 = 220 ..........(1) { p+1 = r => p = r-1 }

Coefficient of (r+1)th term = ⁿC_r =495 ..........(2) { p+1 = r+1 => p = r}

Coefficient of (r+2)th term = ⁿC_r+1 = 792 ..........(3) { p+1 = r

-1

P. Rahul Dev answered this

LetT_r , T_r+1 , T_r+2 be the sucessive terms in the expansionof (1+x)ⁿ

Now T_p+1 in (1+x)ⁿ = ⁿC_px^p => coefficient of (p+1)th term = ⁿC_p

. : Coefficient of rth term = ⁿC_r-1 = 220 ..........(1) { p+1 = r => p = r-1 }

Coefficient of (r+1)th term = ⁿC_r =495 ..........(2) { p+1 = r+1 => p = r}

Coefficient of (r+2)th term = ⁿC_r+1 = 792 ..........(3) { p+1 = r

-5

Lyra answered this

LetT_r , T_r+1 , T_r+2 be the sucessive terms in the expansionof (1+x)ⁿ

Now T_p+1 in (1+x)ⁿ = ⁿC_px^p=> coefficient of (p+1)th term = ⁿC_p

. : Coefficient of rth term = ⁿC_r-1 = 220 ..........(1) { p+1 = r => p = r-1 }

Coefficient of (r+1)th term = ⁿC_r =495 ..........(2) { p+1 = r+1 => p = r}

Coefficient of (r+2)th term = ⁿC_r+1 = 792 ..........(3) { p+1 = r+2 => p = r+1 }

Dividing (2) by (1) we get

ⁿC_r/ⁿC_r-1= 495 / 220

=> n - r +1 / r = 9/4

=> 4(n - r +1) = 9r

=> 4n - 4r +4 = 9r

=> 4n +4 = 9r + 4r

=> 4n - 13r +4 = 0 ...........(4)

Dividing (3) by (2) we get

ⁿC_r+1/ⁿC_r= 792/ 495

=> n - r / r + 1 = 8 / 5

=> 5n - 13r -8 = 0

Subtracting (5) from (4) we get

4n - 13r +4 = 0

5n - 13r -8 = 0 %2

hope this helps you!!!