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The recursive formula
means that, to compute the next value, you have to double the previous one and then add 5.
So, we start with 5. To get the second term, we double it and add five, so we have
Next, we will double 15 and add 5:
So, the answer is B, because it's the only option starting with 5,15,35.
Just to check, let's compute the last step:
Which confirms option B
Answer:
So the quotient is and the remainder is
.
Step-by-step explanation:
We could do this by synthetic division since the denominator is a linear factor in the form .
Since we are dividing by , this is our setup for the synthetic division:
-2 | 1 7 9 -8
| -2 -10 2
______________
1 5 -1 -6
So the quotient is and the remainder is
.
So .
We can also do long division.
x^2+5x-1
____________________
x+2| x^3+7x^2+9x-8
-(x^3+2x^2)
-------------------
5x^2+9x-8
-( 5x^2+10x)
--------------------
-x-8
-(-x-2)
--------------
-6
So we see here we get the same quotient, . and the same remainder,
.
Now let's check our result that:
.
So I'm going to rewrite the right hand side as a single fraction:
.
Now let's focus on multiplying .
We are going to multiply the first term of the first ( ) to every term in the second ( ).
We are also going to multiply the second term of the first ( ) to every term in the second ( ).
---------------------------Combine like terms:
So let's go back where we were in our check of :
We have the exact same thing on both sides so we did good.