The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

To multiply terms with radicals, multiply the coefficients and radicands separately:

3\( \sqrt{9} \) x 9\( \sqrt{7} \)
(3 x 9)\( \sqrt{9 \times 7} \)
27\( \sqrt{63} \)

Now we need to simplify the radical:

27\( \sqrt{63} \)
27\( \sqrt{7 \times 9} \)
27\( \sqrt{7 \times 3^2} \)
(27)(3)\( \sqrt{7} \)
81\( \sqrt{7} \)

To divide fractions, invert the second fraction and then multiply:

\( \frac{3}{6} \) ÷ \( \frac{1}{6} \) = \( \frac{3}{6} \) x \( \frac{6}{1} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{6} \) x \( \frac{6}{1} \) = \( \frac{3 x 6}{6 x 1} \) = \( \frac{18}{6} \) = 3

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-6y⁷ - 8y⁷
(-6 - 8)y⁷
-14y⁷

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.