Answer:
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.
