Question

What is the partial sum
25
∑ -5+13i
i=12

Answer 1

3,297

3,630

3,976

4,335

Answer 2

the sum notation is a linear transformation ... if i recall the definition of a linear transformation correctly

Answer 3

∑ -5+13i

-5∑ + 13 ∑ i

-5(range) + 13 (range(n*(n+1)/2))

Answer 4

range would be defined as: high - low + 1

Answer 5

or, we could translate i from 12 to 0 and add 12 to each i to keep it the same

Answer 6

25
∑ -5+13i
i=12


13
∑ -5+13(i+12)
i=0

there are so many ways we can approach this

Answer 7

i still dont understand it really

Answer 8

if you wanna brute math it into submission, the most fundamental means would be to copy the equation itself a few times such that for each copy you replace the "i" by the values from 12 to 25; then add them all up

Answer 9

-5+13(12)=
-5+13(13)=
-5+13(14)=
-5+13(15)=
....
-5+13(25)=

Answer 10

so after i get each total, do i add all the totals up?

Answer 11

yep

Answer 12

okay

Answer 13

that is the long way to do it, but it works in the end :)

Answer 14

thank you....could i do that for every equation ?

Answer 15

1: -5+13(12)
2: -5+13(13)
3: -5+13(14)
4: -5+13(15)
5: -5+13(16)
6: -5+13(17)
7: -5+13(18)
8: -5+13(19)
9: -5+13(20)
10:-5+13(21)
11:-5+13(22)
12:-5+13(23)
13:-5+13(24)
14:-5+13(25)
--------------
-5(14) + 13(14)(12+25)/2

Answer 16

you can do it for reasonably small equations by hand. the more terms there are the better it is to know the shorter methods

Answer 17

thank you. I found the answer

Answer 18

cool :) what was it ?

Answer 19

3297

Answer 20

yay!! i got that too, so either we both did it right, or we both got it terribly wrong lol

Answer 21

i have another question, and if you dont mind can you please help me?

Answer 22

lol

Answer 23

go ahead and ask

Answer 24

Given the sequence 3, 9, 15, which of the following is equivalent to
8
∑ An
n=5

Answer 25

does it say if the sequence of arith or geoM?

Answer 26

no it doesn't

Answer 27

a1 = 3
a2 = 3 + 6 = 9
a3 = 9 + 6 = 15

so this looks to be that we are adding the same value each time to get the next term. we call that an arithmetic sequence

Answer 28

if we can form the general equation that defines this sequence, we can then do the same thing as the we did on the first question

Answer 29

okay

Answer 30

a1 = 3
a2 = 3 + 6 = 9
a3 = 3 + 6 + 6
3 + 6(2) = 15

an = 3 + 6(n-1) is the equation we seek

Answer 31

okay...im going to try and solve it and see what i get

Answer 32

\[\large \sum_{n=5}^{8}3+6(n-1)\]

Answer 33

1: 3+6(4)
2: 3+6(5)
3: 3+6(6)
4: 3+6(7)
-------
3(4)+6(4)(4+5+6+7)

Answer 34

i got 144

Answer 35

12+24(22) = 12+ 528 is going to be a little bit bigger than 144

Answer 36

144 is one of my answer choices . the highest one is 168

Answer 37

really?

1: 3
2: 9
3: 15
4: 21
..........
5: 27
6: 33
7: 39
8: 45
------
144

hmmm, i wonder what i was thinking about then :)

Answer 38

lol...yea i am about to submit the answers after i finish one more question and i will let you know if it was right or not

Answer 39

They were right...thank you