Step-by-step explanation:
IF THERE ARE FIVE PIECES TO BE SHARED AND EVERYONE MUST HAVE AN EQUAL SHARE THEN EACH PERSON SHOULD GET HALF A PIZZA WHICH IS 1/2. BETWEEN 0 AND 1 IS WHAT THE FRACTION 1/2 WE BE BETWEEN.
Answer:
3, 8, 14, 30, 58
Step-by-step explanation:
As with all formulas, put the numbers in place of the corresponding variables, and do the arithmetic.
![a_1=3\qquad\text{given}\\\\a_2=8\qquad\text{given}\\\\a_3=2a_1+a_2=2(3)+8=14\\\\a_4=2a_2+a_3=2(8)+14=30\\\\a_5=2a_3+a_4=2(14)+30=58](https://tex.z-dn.net/?f=a_1%3D3%5Cqquad%5Ctext%7Bgiven%7D%5C%5C%5C%5Ca_2%3D8%5Cqquad%5Ctext%7Bgiven%7D%5C%5C%5C%5Ca_3%3D2a_1%2Ba_2%3D2%283%29%2B8%3D14%5C%5C%5C%5Ca_4%3D2a_2%2Ba_3%3D2%288%29%2B14%3D30%5C%5C%5C%5Ca_5%3D2a_3%2Ba_4%3D2%2814%29%2B30%3D58)
The first 5 terms of the sequence are 3, 8, 14, 30, 58.
To factor this fraction, you have be be aware of two special factoring formula:
a^3<span> + </span>b^3<span> = (</span>a<span> + </span>b)(a^2<span> – </span>ab<span> + </span>b^2<span>)
</span><span>(a+b)³ = a³ + 3a²b + 3ab² + b³
You can see the top part in this case is (x+y)^3, and the bottom (denominator) can be factor into (x+y)(x^2-xy+y^2)
we can cancel (x+y), so what we have left is (x+y)^2/(x^2-xy+y^2)
or (x^2+2xy+y^2)/(x^2-xy+y^2)
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