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High School Mathematics - 2
7.4 General Term (Tr+1)

Suppose we have to find the (r+1)th term in the expansion of (x+y)n
In its expansion we find that
T3 = nC2 xn-2y2
T4 = nC3 xn-3y3
We can see that all these terms have the following properties.
  1. The suffix of C is one less than the number of terms.
  2. The power of the first factor x is equal to the difference of the upper and lower suffixes of C.
  3. The power of the second factor y and the suffix of C are same.
  4. The sum of the power of x and y is equal to the index of the given binomial.
Hence (r+1)th term is given by
Tr+1 = nCrxn-ryr

Example: Find the tenth term in the expansion of (2x-y)11.
Solution: T10 = T9+1 = 11C9(2x)11-9(-y)9 = 11C2(2x)2(-y)9
Answer: -220x2y9

Directions: Answer the following.
Q 1: If the 21st and 22nd terms in the expansion of (1+x)44 are equal. Find the value of x.

Q 2: Find the sixth term of (2x-1/x2)7

Q 3: Find the middle term of (a/x+x/a)10

Q 4: find the value of (2x2-1/x)1/2

Q 5: Find the term independent of x in the expansion of (x2-2/x3)5

Q 6: Find the middle term of (2x-1/y)8

Q 7: Find the fifth term in (2a+3b)12. Evaluate it when a = 1/3, b = 1/4

Q 8: In the expansion of (1+x)11, the fifth term is 24 times the third term. Find the value of x.

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Question 10: This question is available to subscribers only!

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