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10.) Jamila is making a triangular wall
with building blocks. The top row has one
block, the second row has three blocks, the
third row has five, and so on. How many
rows can she make with a set of 100
blocks?​

Respuesta :

LODZYBELLS

Answer:

the amount of rows she can make with a set of 100 blocks is 10 rows

Step-by-step explanation:

this question is an example of a Arithmetic Progression

I.e 1, 3, 5, ............ 100

therefore,

1st term (a) = 1

common difference (d) = 2 (either 3 - 1 or 5 - 3)

[tex]s_{N} = 100[/tex]

from the formula

[tex]\frac{(2a+(N-1)d)N}{2} =s_N}[/tex]

[tex]\frac{(2(1)+(N-1)(2))N}{2} =100}[/tex]

[tex]\frac{(2+2N-2)N}{2} =100}[/tex]

[tex]\frac{2N^{2} }{2} = 100[/tex]

[tex]N^{2} = 100[/tex]

by taking the square root of both sides

N = [tex]\sqrt{100}[/tex]

N = 10

adioabiola

The number of rows Jamila can make with a set of 100 blocks is 10 rows

Given:

Row 1 = first term, a = 1 block

Row 2 = second term = 3 blocks

Row 3 = third term = 5 blocks

Common difference, d

= secod term - first term

= 2 blocks

n = number of rows

So,

S(n) = n/2 {2a + (n - 1)d}

100 = n/2 {2×1 +(n - 1)2}

100 = n/2 {2 + 2n - 2}

100 × 2 = n(2n)

200 = 2n²

n² = 200/2

n² = 100

n = √100

n = 10

Therefore, number of rows Jamila can make with a set of 100 blocks is 10 rows

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