Final answer:
The sixth term in the binomial expansion of (5y+3)¹⁰ is represented by 10C5·(5y)⁵·3⁵, corresponding to the formula for the (k+1)th term in the expansion.
"the correct option is approximately option A"
Step-by-step explanation:
The sixth term in the binomial expansion of (5y+3)¹⁰ is given by the general formula for the binomial theorem, which in simpler terms is written as:
T(k+1) = nCk · (first term)^(n-k) · (second term)^k
Where T(k+1) is the (k+1)th term, nCk represents the binomial coefficient, and n is the power of the expansion. To find the sixth term, we set k to 5, since the first term is T(1) when k=0.
So for the sixth term (k=5), we get:
T(6) = 10C5 · (5y)^(10-5) · 3^5
Therefore, the correct expression for the sixth term is:
10C5·(5y)⁵·3⁵
This matches one of the given options:
a. 10C5·(5y)⁵·3⁵