# arrow_back Find x using quadratic 7;10;x;22;31

23 views
Quadratic patterns

## 1 Answer

Best answer

Best answer

Answer:

$x=15$

Explanation:

Given that the sequence is quadratic then it implies that the 2nd order difference is constant.

The sequence is:

$7;10;x;22;31$

First Difference i.e. $a_{n+1}-a_n$

Let:

$a=10-7=3$

$b=x-10$

$c=22-x$

$d=31-22=9$

Second Difference:

Since the sequence is quadratic, let the constant difference be $y$

$b-3=y$

$c-b=y$

$d-c=9-c=y$

Using the above information (simultaneous equations), we can solve for $y$.

Making $c$ subject of formula in $9-c=y$ gives $c=9+y$.

Substituting for $c$ in $c-b=y$ gives $b=9-2y$

Substituting for $b$ in $b-3=y$ gives $y=2$.

Now that we know that $y=2$ we can deduce the value of $x$ by rewriting the first differences that include an $x$

First Differences

$x-10 =5$ therefore $x=15$

$22-x = 7$ therefore $x=15$

by Gold Status
(30,543 points)

## Related questions

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Using the quadratic formula, solve the quadratic equation: $x-31 / x=0$
1 answer 150 views
Using the quadratic formula, solve the quadratic equation: $x-31 / x=0$Using the quadratic formula, solve the quadratic equation: $x-31 / x=0$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the quadratic equation $x^{2}+7 x+12=0$ by factorization method.
1 answer 180 views
Solve the quadratic equation $x^{2}+7 x+12=0$ by factorization method.Solve the quadratic equation $x^{2}+7 x+12=0$ by factorization method. ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Using the quadratic formula, solve the quadratic equation: $x^{2}-9 x+14=0$
1 answer 185 views
Using the quadratic formula, solve the quadratic equation: $x^{2}-9 x+14=0$Using the quadratic formula, solve the quadratic equation: $x^{2}-9 x+14=0$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Using the factoring method, solve the quadratic equation: $2 x^{2}-3 x=0$
1 answer 281 views
Using the factoring method, solve the quadratic equation: $2 x^{2}-3 x=0$Using the factoring method, solve the quadratic equation: $2 x^{2}-3 x=0$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Using the factoring method, solve the quadratic equation: $x^{2}+4 x+4=0$
1 answer 184 views
Using the factoring method, solve the quadratic equation: $x^{2}+4 x+4=0$Using the factoring method, solve the quadratic equation: $x^{2}+4 x+4=0$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve for $x$ in the quadratic equation $x^{2}+10 x+8=0$
1 answer 26 views
Solve for $x$ in the quadratic equation $x^{2}+10 x+8=0$Solve for $x$ in the quadratic equation $x^{2}+10 x+8=0$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Use the quadratic formula to solve the equation $2x^2-3x+10=53$
1 answer 117 views
Use the quadratic formula to solve the equation $2x^2-3x+10=53$Use the quadratic formula to solve the equation $2x^2-3x+10=53$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the quadratic equation $x^2-6x=0$
1 answer 39 views
Solve the quadratic equation $x^2-6x=0$Solve the quadratic equation $x^2-6x=0$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the quadratic equation $3 x^{2}+2 x-8=0$
1 answer 149 views
Solve the quadratic equation $3 x^{2}+2 x-8=0$Solve the quadratic equation $3 x^{2}+2 x-8=0$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the following quadratic equation by completing the square $$9 x^{2}+12 x-3=0$$
1 answer 108 views
Solve the following quadratic equation by completing the square $$9 x^{2}+12 x-3=0$$Solve the following quadratic equation by completing the square $$9 x^{2}+12 x-3=0$$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the following quadratic equation by the square root property. $$(2 x-1)^{2}=9$$
0 answers 79 views
Solve the following quadratic equation by the square root property. $$(2 x-1)^{2}=9$$Solve the following quadratic equation by the square root property. $$(2 x-1)^{2}=9$$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the following quadratic equation by the zero-factor property. $$3 x^{2}-x=14$$
1 answer 128 views
Solve the following quadratic equation by the zero-factor property. $$3 x^{2}-x=14$$Solve the following quadratic equation by the zero-factor property. $$3 x^{2}-x=14$$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve the quadratic equation $x^2 +3x+1=(x-2)^2$
1 answer 107 views
Solve the quadratic equation $x^2 +3x+1=(x-2)^2$Solve the quadratic equation $x^2 +3x+1=(x-2)^2$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve for $x$ in the equation $\sqrt{2-7 x}+2 x=0$
1 answer 111 views
Solve for $x$ in the equation $\sqrt{2-7 x}+2 x=0$Solve for $x$ in the equation $\sqrt{2-7 x}+2 x=0$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve $6-7 x^{2}=0(a=-7, b=0, c=-6)$
1 answer 92 views
Solve $6-7 x^{2}=0(a=-7, b=0, c=-6)$Solve $6-7 x^{2}=0(a=-7, b=0, c=-6)$ ...
close