Find the 5th term in the binomial expansion. $$( a + \sqrt { 3 } t ) ^ { 9 }$$
A) $\quad 126 a ^ { 5 } t ^ { 4 }$
B) $\quad 2,536 a ^ { 6 } t ^ { 3 }$
C) $\quad 2,536 a ^ { 5 } t ^ { 4 }$
D) $\quad 1,134 a ^ { 4 } t ^ { 5 }$
E) $\quad 1,134 a ^ { 5 } t ^ { 4 }$

Question

Quizplus · Accepted Answer

The 5th term in the binomial expansion of $(a + \sqrt{3}t)^9$ can be found using the formula for the $k+1$th term: $_nC_k \cdot a^{n-k} \cdot b^k$, where $n$ is the power of the binomial, $a$ and $b$ are the terms of the binomial, and $k$ is the term number minus 1. For the 5th term, $k = 4$, so we calculate $_9C_4 \cdot a^{9-4} \cdot (\sqrt{3}t)^4$. This simplifies to $126 \cdot a^5 \cdot (3^2)t^4 = 126 \cdot a^5 \cdot 9t^4 = 1134a^5t^4$.

Find the 5th Term in the Binomial Expansion (a+3t)9( a + \sqrt { 3 } t ) ^ { 9 }(a+3​t)9

Find the 5th Term in the Binomial Expansion $( a + \sqrt { 3 } t ) ^ { 9 }$