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Binomial Theorem — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSBinomial Theorem1 Mark
Question
Middle term in the expansion of (a3 + ba)28 is _________.
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Answer

Middle term in the expansion of (a3 + ba)28 is $=\ ^{28}\text{C}_{14}\text{a}^{56}\text{b}^{14}$.
Solution:
Given expression is (a3 + ba)28.
Since index is n = 28 (even)
So, there is only one middle term which is $\Big(\frac{28}{2}+1\Big)^\text{th}$ term or 15th term.
$\therefore$ Middle term, $\text{T}_{15}=\text{T}_{14+1}=\ ^{28}\text{C}_{14}(\text{a}^3)^{28-14}(\text{ba})^{14}$
$=\ ^{28}\text{C}_{14}\text{a}^{42}\text{b}^{14}\text{a}^{14}=\ ^{28}\text{C}_{14}\text{a}^{56}\text{b}^{14}$

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