The two successive terms in the expansion of $(1 + x)^{24}$ whose coefficients are in the ratio $4 : 1$ are

t_{18}, t_{19}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

t_{19}, t_{20}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

t_{20}, t_{21}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

t_{21}, t_{22}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $t_{20}, t_{21}$
Let the two successive terms be $T_{r}$ and $T_{r + 1}$ .
Therefore it is given that
$\frac{T_{r}}{T_{r + 1}} = \frac{4}{1}$
or
$T_{r} = 4 T_{r + 1}$ .
$^{24} C_{r - 1} = 4^{24} C_{r}$
$\frac{1}{24 - (r - 1)} = \frac{4}{r}$
$r = 96 - 4 r + 4$
$5 r = 100$
$r = 20$
Hence the two consecutive terms are $T_{20}$ and $T_{21}$

Suggest Corrections

Similar questions

Q. Two successive terms in the expansion of

(1 + x)^{24}

whose coefficients are in the ratio 4 : 1 are

If t(n) represents the $n^{t h}$ term of an AP, then which of the following is always true?

Two successive terms in the expansion of $(1 + x)^{24}$ , whose coefficients are in the ratio 4:1 are $(r + 1)^{t h}$ and $(r)^{t h}$ ,r <15. Find the value of r

___

Q. The two successive terms in the expansion of

(1 + x)^{24}

whose coeff are in ratio

1 : 4

are

Q. The two successive terms in the expansion of (1 + x)²⁴ whose coefficients are in the ratio 1 : 4 are
(a) 3^rd and 4^th
(b) 4^th and 5^th
(c) 5^th and 6^th
(d) 6^th and 7^th

Join BYJU'S Learning Program

The two successive terms in the expansion of (1+x)24 whose coefficients are in the ratio 4:1 are

The correct option is A t20,t21Let the two successive terms be Tr and Tr+1.Therefore it is given that TrTr+1=41orTr=4Tr+1.24Cr−1=424Cr124−(r−1)=4rr=96−4r+45r=100r=20Hence the two consecutive terms are T20 and T21

The two successive terms in the expansion of $(1 + x)^{24}$ whose coefficients are in the ratio $4 : 1$ are