Sonia has 120 blocks. she decides to stack up all the blocks so that each row has one less block than the row below. She wants to end up with just 1 block on top. How many blocks should she put in the bottom row?

15 blocks

Step-by-step explanation:

Step 1

This is an Arithmetic sequence. We are using the formula below.

aₙ = a + ( n - 1) d Equation 1

Where:

a = First term

d = Common difference

n = number of term

We are told in the question that each row has one less block

Therefore,

aₙ = 1

d = -1 ( one less block)

a = a

aₙ = a + ( n - 1) d

1 = a + ( n - 1) -1

1 = a + ( -n + 1)

1 = a - n +1

a - n + 1 - 1 = 0

a - n = 0

a = n

Therefore, a = n

Step 2

The next step would be to solve the question using the sum of the arithmetic sequence formula

Sn = n/2( a + 1) Equation 2

Where these values have already been given in the question

Sn = 120

a = n ( from the first step)

We are to solve for a

We would substitute n for a in Equation 2

Therefore, we have

Sn = n/2( a + 1)

120 = a/2(a + 1)

Cross multiply

120 × 2 = a(a + 1)

240 = a² + a

a² + a - 240 = 0

Using factorisation to solve the quadratic equation

a² -15a +16a -240 = 0

(a² - 15a) + (16a -240) = 0

a(a -15) + 16(a - 15) = 0

Hence, we have

(a- 15) (a + 16) = 0

a - 15 = 0

a = 15

a + 16 = 0

a = - 16

a = 15, -16

We pick the positive number, which is a = 15

Therefore, the number of blocks Sonia  should put in the bottom row is 15 blocks.

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step-by-step explanation:

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