Following this pattern, type a number to show how many bags of wheat there will be on the sixth square. Will pay 14 points

The number of bags of wheat that will be on the sixth square is 32wheats

The amount of wheat in each square are expressed in geometric sequence as shown.

1, 2, 4, 8, 16,

Geometric sequence is a sequence where the ratio of the succeeding and the preceding term is equal to a common ratio.

The nth term is expressed as

Tn = ar^{n-1}

a is the first term

r is the common quantity

n is the number of terms

a = 1

n = 6 (sixth square)

r = 4/2 = 2/1 = 2

Substitute the given values into the formula

T6 = 1(2)^{6-1}

T6 = 2^5

T6 = 32

Hence the number of bags of wheat that will be on the sixth square is 32wheats

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hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb