Question #99b2b

1 Answer
Nov 8, 2016

Answer:

The question only asks for the missing number which is 34

Explanation:

When faced with a sequence you first need to establish if is arithmetic or geometric.

By example

Arithmetic:
Progresses by some variant on addition or subtraction of a constant

Geometric:
Progresses by some variant on the multiplication or division of some constant raised to a power.

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Observe that:

#40-37=3#
#31-28=3#
#28-25=3#

This indicates that it is a arithmetic progression and that as it is reducing the change is #-3#

#color(green)("So the missing number is "37-3=34#

Check: #34-3=31 color(red)(larr"Confirmed")#
~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("As this is the algebra section - Developing the equation")#

Let the first term be #a_1=40#

Let the #i^("th") # term be #a_i#

#a_1=a_1-0=40#
#a_2=a_1-3=37#
#a_3=a_1-3-3=34#
#a_4=a_1-3-3-3=31#

By observation we deduce that:

#color(blue)(=>a_i=a_1-3(i-1) = 40-3(i-1))#

check:
#=>a_1=40-3(1-1) = 40-0=40#