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Sagot :
The Required sequence of the arithmetic progression will be,
= 21, 18, 15, 12, 9, 6
According to the question,
The term that is given is the third term of the sequence = 15
Let the fourth term of the sequence be = x
Let the sixth term of the sequence be = [tex]\frac{x}{2}[/tex]
So let's make a structure of the sequence=
_, _, 15, x, _, [tex]\frac{x}{2}[/tex]
Let us consider d as the difference between two terms,
d = x - 15
x = 15 + d -------- equation 1
According to the arithmetic progression if we add the difference of x and 15 into x it will give us the fifth term
let the fifth term be y
x + d = y ------- equation 2
And similarly adding the difference d to y will give the sixth term that is [tex]\frac{x}{2}[/tex]
y + d = [tex]\frac{x}{2}[/tex] ------- equation 3
substituting the value of y from equation 2 to equation 3
x + d + d = [tex]\frac{x}{2}[/tex]
x + 2d = [tex]\frac{x}{2}[/tex]
2d = - x + [tex]\frac{x}{2}[/tex]
d = - [tex]\frac{x}{4}[/tex]
Now substituting the value of d into equation 1,
x + 15 + (- [tex]\frac{x}{4}[/tex] )
x + [tex]\frac{x}{4}[/tex] = 15
[tex]\frac{5x}{4}[/tex] = 15
x = [tex]\frac{15 *4}{5}[/tex]
x= [tex]\frac{60}{5}[/tex]
x = 12
Now we know that the third term of the series x = 12
Similarly the sixth term = [tex]\frac{x}{2}[/tex]
= [tex]\frac{12}{2}[/tex]
= 6
So as we can see that the total difference between each term is = 3
Therefore, the required sequence = 21, 18, 15, 12, 9, 6
To know more about Arithmetic Progression,
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