Question

Question #99b2b

Answer 1

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")`
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`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`