The series' value is maximized if the sum only consists of positive terms. Notice that each term in the sum takes the form 4<em>n</em> + 1 for integer <em>n</em>. This means the smallest positive integer that the sum can involve is 1, so the maximum value is
<em>S</em> = 29 + 25 + 21 + … + 9 + 5 + 1
Reversing the order of terms gives the same sum,
<em>S</em> = 1 + 5 + 9 + … + 21 + 25 + 29
Adding terms in the same positions gives us twice this sum,
2<em>S</em> = (29 + 1) + (25 + 5) + (21 + 9) + … + (1 + 29)
Notice how each grouped sum adds to 30. There are 8 terms in the sum, since 4<em>n</em> + 1 = 29 when <em>n</em> = 8. So
2<em>S</em> = 8 × 30 = 240 ===> <em>S</em> = 120
Answer:
C. Linear
Step-by-step explanation:
Because the amount of money is increasing by a constant rate of $4.
8 baseball cards + 5 football cards= 13 cards
8 baseball cards per every 13 total cards.
78÷13=6
6×8= 48
48 Baseball Cards in total
Answer: A= 70 b=135 x=10
Step-by-step explanation:
A+110=180 because a straight line is always 180.
a triangle should equal 180 as well so you would put A+(5x-5)+(6x+5)=180. the +5 and -5 would cancel each other out. So you would be left with 70+5x+6x=180 (combine like terms) 70+11x+180 subtract 70 from both sides and will leave you with 11x=110 divid by 11 and x=10. plug 10 in for 5x-5. That will give you 45 and then 180-45=135.
