What is the fifth term of (2x + y)^8?

Expansion for there will be 9 terms.

(a+b) ^n =nco a^n b^o+ nc1 a^(n-1) b^1+nc2 a^(n-2) b^2+nc3 a(n-3) b^3+nc4  a^(n-4) b^4+ncn a^o b^n.

5th term of  (2x+y)^8 = ?  

5th term is nC4 a^(n-4) b^4

a=2x, b=y, n=8

therefore 8C4 (2x)^(8-4)  (y)^4

8!/((8-4)! 4!) (2x)^4 y^4

40320/576  (16 x^4 ) (y^4)

70 (16x^4)(y^4)

1120 X^4 Y^4

Step-by-step explanation:

95.03 is the answer. hope this !

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt