Which is one way to check 102 ÷ 6 = 17
a. 105 ÷ 10 = 10.5
b. 100 ÷ 5 = 20
c. 102 ÷ 10 = 10.2
d. 105 ÷ 5 = 21

Part 1:
a. Number of people in the seventh row will be as follows:

d=2
a1=1
n=7
thus the number of people in the 7th row will be obtained using the explicit formula:
an=a1+(n-1)d
a7=1+(7-1)2
a1=1+12
a1=13

b. Total number of people in 7 rows will be calculated using the formula:
sn=n/2(a1+an)
plugging in the values:

s7=7/2(1+13)
s7=7/2(14)
s7=49

c. Total number of people required to make 10 rows will be:
n=10
a1=1

a10=1+(10-1)2
a10=1+18
a10=19
thus
s10=10/2(1+19)
s10=100
It will take 100 children

d. To get the number of rows the Simpsons Pyramid had we shall use the explicit formula:
an=a+(n-1)d
d=4
a1=1
an=37
plugging in the values we get:
37=1+(n-1)4
solving for n:
36=4n-4
40=4n
n=10
thus the number of rows would be 10 

e. Total number of people will be:
d=4
n=10
a1=1
Sn=n/2(a1+an)
Sn=10/2(1+37)
Sn=190

PART 2: Geometric sequence and series
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