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Question
Find the 7th term in the expansion of \[\left( 3 x^2 - \frac{1}{x^3} \right)^{10}\] .
Solution
We need to find the 7th term of the given expression.
Let it be T7
Now, we have \[T_7 = T_{6 + 1}\]
\[= ^{10}{}{C}_6 (3 x^2 )^{10 - 6} \left( \frac{- 1}{x^3} \right)^6 \]
\[ =^{10}{}{C}_6 \left( 3^4 \right)\left( x^8 \right)\left( \frac{1}{x^{18}} \right)\]
\[ = \frac{10 \times 9 \times 8 \times 7 \times 81}{4 \times 3 \times 2 \times x^{10}} = \frac{17010}{x^{10}}\]
Thus, the 7th term of the given expression is \[\frac{17010}{x^{10}}\]
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