Let <em>x</em> be the first number in the sequence, so the first three numbers are
{<em>x</em>, 0.5<em>x</em>, 0.5²<em>x</em>}
Then
{<em>x</em>/4 + 10, 0.5<em>x</em> - 10, 2(0.5²<em>x</em>) + 10}
is arithmetic, so there is some constant<em> c</em> such that
0.5<em>x</em> - 10 = <em>x</em>/4 + 10 + <em>c</em> ==> <em>x</em>/2 - 10 = <em>x</em>/4 + 10 + <em>c</em>
2(0.5²<em>x</em>) + 10 = 0.5<em>x</em> - 10 + <em>c</em> ==> <em>x</em>/2 + 10 = <em>x</em>/2 - 10 + <em>c</em>
Solve the second equation for <em>c</em> :
<em>x</em>/2 + 10 = <em>x</em>/2 - 10 + <em>c</em>
<em>c</em> = 20
Substitute this into the first equation and solve for <em>x</em> :
<em>x</em>/2 - 10 = <em>x</em>/4 + 10 + 20
<em>x</em>/4 = 40
<em>x</em> = 160
Then the terms are
{160, 80, 40}
Consider the given statement:
8+3.4=3.4+8
We have to identify the property used in this statement.
1. Associative Property of Addition: Let a,b and c be three real numbers. This property states that
. This property is not used in the given statement.
2. Inverse property of addition: A number 'a' is said to have an inverse '-a' if
. This property is not used in the given statement.
3. Inverse property of multiplication: A number 'a' is said to have an inverse '
' if
. This property is not used in the given statement.
4. Commutative property of addition: Let 'a' and 'b' be two real numbers. This property states that
.
In the given statement, 8+3.4=3.4+8
which is expressed as 8+12 = 12+8, this statement holds commutative property of addition as whether 8 is added to 12 or 12 is added to 8, the result is same.
So, Commutative property of addition is illustrated in this statement.
The answer greater is probably 100