Find the indicated coefficient or term.
-The 5th term in the expansion of ( $( 2 x + 5 ) ^ { 5 }$
A) 15,625
B) 2,500x2
C) 1,250x
D) 6,250x

Question

Quizplus · Accepted Answer

The 5th term in the expansion of $(2x + 5)^5$ can be found using the binomial theorem: $T_{k+1} = \binom{n}{k} (a)^{n-k} (b)^k$. For the 5th term, k=4, n=5, a=2x, b=5. So, $T_5 = \binom{5}{4} (2x)^{1} (5)^4 = 5 \cdot 2x \cdot 625 = 6,250x$.

Find the Indicated Coefficient or Term (2x+5)5( 2 x + 5 ) ^ { 5 }(2x+5)5

Find the Indicated Coefficient or Term $( 2 x + 5 ) ^ { 5 }$