Question

Evaluate
8
E - n/4
n=2

Answer 1

@ganeshie8 . do you know what this is ?

Answer 2

?

Answer 3

You wanto evaluate \(8E(-n/4)\) when n=2 ha ?

Answer 4

sorry n/5

Answer 5

easy, is that -n/4 or -n/5 ?

Answer 6

-n/5

Answer 7

\[\sum_{n=2}^{8} -\frac{ n }{ 5 }\]

Answer 8

\(\sum_{n=2}^{8} - \frac{ n }{ 5 } \)

Answer 9

uhh... why i am not getting n=2 in bottom os SUM notation

Answer 10

im not sure. :(

Answer 11

ok, its called SUMMATION

Answer 12

∑ this symbol is called summation symbol

Answer 13

yes. i know .

Answer 14

what it says is, you need to take sum. il show a simple example

Answer 15

okk

Answer 16

\(\large \sum_{n=1}^{3} n \)

Answer 17

\(\large \sum_{n=1}^{3} n = 1 + 2 + 3\)

Answer 18

thats one example. you just need to take sum, replacing n wid 1, 2, 3 each time

Answer 19

What a sigma notation tells is that we add a series of number which add up to something. So in your case it is asking what does -n/5 equal to when n starts at 2 and ends at 8. So you would add -(2/5)-(3/5)-(4/5)-(5/5)-(6/5)-(7/5)-(8/5)= ? Add those up and the sum is your answer.

Answer 20

use that example, and see if u can solv ethe present problem

Answer 21

wait so i add 2 , 3, 4, 5, 6,7,8 ?

Answer 22

you're not given n, you're given -n/5

Answer 23

\(\sum_{n=2}^{8} -\frac{ n }{ 5 } = \frac{-2}{5} + \frac{-3}{5} +\frac{-4}{5} +\frac{-5}{5} +\frac{-6}{5} +\frac{-7}{5} +\frac{-8}{5} \)

= ?

Answer 24

ohhh okk . sooo -25/n ?

Answer 25

im getting -35/5

Answer 26

which equals -7

Answer 27

oopss i counted wrong. okk yess i got -35/5=-7

Answer 28

ha

Answer 29

is that all ?

Answer 30

thats all to SUMMATION or SIGMA notation.

Answer 31

when u see that symbol, just add repeatedly... like above

Answer 32

ohh okk (: . so my answer is -7 ?

Answer 33

correct !

Answer 34

oh that was pretty simple. i going to try the next few on my own. then ill shhow you (;

Answer 35

sounds very good :)

Answer 36

\[\sum_{n=2}^{8}-(n-5)\]
Add -2/5 , 3/5, 4/5, 5/5, 6/5,7/5,8/5
= -35/5
=-7
\[\sum_{n=3}^{7}\frac{ n }{ 4 }\]
Add 3/4 , 4/4, 5/4, 6/4,7/4
=25/4

Answer 37

in the first problem, you mean -n/5 ?

Answer 38

noo i realized i wrote it wrong.

Answer 39

which one is correct, -(n-5) or -n/5 ?

Answer 40

-(n-5)

Answer 41

then wat u did above is not correct. do it again from scratch

Answer 42

am i supposed to use the same concept ?

Answer 43

yes same concept, just keep adding, replacing n each time

Answer 44

ok , can you tell me what i did wrong ?

Answer 45

whole thing is wrong for that q

Answer 46

however, u did the next q perfect ! :)

Answer 47

its like this :-

Answer 48

\(\sum_{n=2}^{8}-(n-5) \\ \\ = -(2-5) - (3-5) - (4-5) - (5-5) - (6-6) - (7-7) - (8-8)\)

Answer 49

ok yay for # 2 (: . now number 1. do i add now ?

Answer 50

yes

Answer 51

wait would i simplify whats in the parenthesis first ? like
(2-5)=-3 ?

Answer 52

correct ! first simplify things inside parenthesis

Answer 53

ok i got -(-3)-(-2)-(-1)-0-1-2-3

Answer 54

it wud become :-

\(-(-3) - (-2) - (-1) - (0) - (1) - (2) - (3)\)

Answer 55

i got the same :)

Answer 56

simplify completely

Answer 57

0 ?

Answer 58

Yes !

Answer 59

(:. your so smart !

Answer 60

noo you're smart to learn these in few minutes oly :D

Answer 61

Thankyouuu (::. okk a few more before my test.
Given the arithmetic sequence –6, 1, 8…, evaluate\[\sum_{n=9}^{12_{}} a _{n}\]

Answer 62

how would i plug in -6,1,and 8

Answer 63

It is asking you to find the sum of terms from 9 to 12

Answer 64

this is the sequence : –6, 1, 8....

Answer 65

first term, a = -6
common difference, d = ?

Answer 66

+7 ? that how it goes from -6 to 1 to 8 .

Answer 67

thats right !

Answer 68

ok (:. so whats the next step ?

Answer 69

\(\sum_{n=9}^{12_{}} a _{n} = a_9 + a_{10} + a_{11} + a_{12}\)

Answer 70

find \(a_9, a_{10}, a_{11}, \ \text{and} \ a_{12}\) of the sequence

Answer 71

\(a_9 = -6 + (9-1) 7 = -6 + 56 = 50\)

Answer 72

ohhh ok. what formula did you use ?

Answer 73

since common difference is 7,

\(a_{10} = 50+7 = 57\)

\(a_{11} = 57+7 = 64\)

\(a_{12} = 64+7 = 71\)

Answer 74

add all these together. (il give u the formula in the end)

Answer 75

add 57+64+71 ?

Answer 76

dont forget \(a_9\)

Answer 77

sooo 50+57+64+71 = 242

Answer 78

thats right !

Answer 79

Now getting back to the formula used when doing below :-

\( a_9 = -6 + (9-1) 7 = -6 + 56 = 50 \)

Answer 80

Ive used the formula for "nth term in arithmetic sequence" :

\(a_n = a + (n-1)d\)

a = first term
d = common difference

Answer 81

ohh okk (:. so 242 was the answer. ? ok im going to attemt the next one on myh own. brb (:

Answer 82

good luck ! il be right here :)

Answer 83

and yes 242 is the answer

Answer 84

Given the arithmetic sequence 23, 17, 11 …, evaluate \[\sum_{n=4}^{9} a _{n}\]

a4+a5+a6+a7+a8+a9
a4=23+(4-1)-6=23+3(-6)=23+-18=5
a5=5+-6=-1
a6= -1+-6=-7
a7=-7+-6=-13
a8=-13+-6=-19
a9=-19+-6=-25
5+-1+-7+-13+-19+-25=-60

Answer 85

Looks perfect !

Answer 86

u knw, theres another way to do this

Answer 87

we will try it next time ok

Answer 88

okkk (:.
Using sigma notation, describe the total length of 7 pictures hung side-by-side. Then find the total length the pictures occupy along the wall if the first picture has a length of 10 inches and the length of each successive picture is 4 inches longer than the previous one.

Answer 89

is sigma notation what we were doing ?

Answer 90

Yes. since we need to add 7 pictures, it wud be :-

\(\sum_{1}^7 a_n \)

Answer 91

then, it tells us that, first pic has a length of 10 inches, that means, a = 10

Answer 92

i mean, \(a_1 = 10\)

Answer 93

since each successive pic is 4 inches extra, d = 4

Answer 94

so, the sequence of lengths wud be :-

10, 14, 18....

Answer 95

and there wud be 7 pics, right ?

Answer 96

So, n = 7

Answer 97

\(\sum_{1}^7 a_n = a_1 + a_2 + ...... + a_7\)

Answer 98

so i would start of with a10, a14,a18 right ?