Answer:
To rewrite your question, you are looking for the smallest that fulfills the inequality:
∑=1>250
First, we must find the sequence in explicit form. We can think of it as a line we are trying to get the slope-intercept form of. We have the points (1, 3) and (2, 8). Therefore, the slope is 8−32−1=51=5 . Now we just need the y-intercept. We can find it through substitution:
=5+
In order to solve for , we can plug in one of the points that we were already given. I will choose the point (1, 3). Note that this point just means that when =1 , =3 .
3=5(1)+
3=5+
=−2
Now for the original question.
∑=1(5−2)>250
((5(1)−2)+(5()−2)2)>250
(5+12)>250
522+12>250
2+15>100
2+15+1100>100+1100
(+110)2>100+1100
(+110)2>10001100
+110>±10001100‾‾‾‾‾‾‾√
+110>±11010001‾‾‾‾‾‾√
>−110±11010001‾‾‾‾‾‾√
Since we are looking for the smallest value, we will subtract for the plus or minus sign.
>−110−11010001‾‾‾‾‾‾√≈−10
Since that is negative, we will have to add instead.
>−110+11010001‾‾‾‾‾‾√≈9.9
Therefore, the smallest integer that makes sense and satisfies the inequality is 10.
So, the first 10 numbers must be added.
Honestly, it would have been quicker just to brute-force this.
Step-by-step explanation:
Have a good day
