Question

What is the value of the sum 5 + 10 + 15 + ... + 95 + 100?

Answer 1

1050

Answer 2

Is there an equation or formula to solve?

Answer 3

\[S_n = \frac{n}{2} (\text{First Term} + \text{Last Term})\]

It's an Arithematic Progression, maybe you know that already.

Answer 4

Arithmetic*

Answer 5

Ah! Thank you. Yes I just could not think of it for nothing!

Answer 6

No Problem

Answer 7

\[\sum_{i=1}^{20}5i=5\sum_{i=1}^{20}i=5 \cdot \frac{20(20+1)}{2}=5 \cdot 10(20+1)=50(21)=1050\]

Answer 8

i dont understand through ishaans formula. and myins is more than confusing!

Answer 9

lol what

Answer 10

no not confusing
we have
5(1+2+3+...19+20)

Answer 11

\[=5 \cdot \frac{20(20+1)}{2}\]

Answer 12

what is n

Answer 13

\[\sum_{i=1}^{k} i=\frac{k(k+1)}{2}\]

Answer 14

is n 5?

Answer 15

n is the number of terms in ishaan's expression

Answer 16

uhh?

Answer 17

o i see

Answer 18

tht would be 5/2(5+100)

Answer 19

i bet satellite is fixing to say something to put down my way

Answer 20

\[5\sum_{k=1}^{20}k=5\times \frac{20\times 21}{2}\]
\[5\times 10\times 21\]

Answer 21

lol

Answer 22

no no i like it. what else would you do?

Answer 23

ishaan's way

Answer 24

uhhh

Answer 25

our his expression works great too

Answer 26

or*

Answer 27

satellite i have no clue what tht funky llooking E stands for

Answer 28

sum

Answer 29

chopper it means we are adding a whole bunch and we don't want to write down every term of the finite series

Answer 30

but what is that picture? andy warhol painting portraits of tourists at the beach?

Answer 31

i can make tht^

Answer 32

cazil after you seen the E looking thing
its actually called sigma

Answer 33

have you*
i can't type

Answer 34

example:
\[\sum_{i=1}^{6}f(x_i)=f(x_1)+f(x_2)+f(x_3)+f(x_4)+f(x_5)+f(x_6)\]

Answer 35

I have seen it before. But am not very familiar with it yet. The arithmetic progression I know though.

Answer 36

it comes very useful when you have infinite series

Answer 37

you will see it more if you do more mathematics

Answer 38

Did the formula help? I dislike memorizing formulas!

Answer 39

myin did u delete my pic?

Answer 40

it was fine if u did

Answer 41

Maybe. I was trying to stick to the topic. Sorry.

Answer 42

it was fine! i was just joking around

Answer 43

I know.

Answer 44

:) i still dont understand the whole ishaan formula tho..

Answer 45

which part?

Answer 46

you get the n part right?

Answer 47

the formula it self
no the n part
if 5=n then it still needs to be divided by 2 right?

Answer 48

well n=20

we have 20 terms

ishaan's formula we have
\[20 \cdot \frac{5+100}{2}=10(105)=1050\]

Answer 49

but it says n/2

Answer 50

yes i divided by 2

Answer 51

no i mean that 20 should be divided by 2

Answer 52

kc i... generally don't recommend cramming, but since it's a special case, i advise you to learn the formula and you can deduce and understand it later.

Answer 53

no i am trying to make a point here. im learning

Answer 54

@ myin, u wrote (5+100)/2 but shouldnt it be 20/2?

Answer 55

no have a look at the formula again
\[S_n = \frac{n}{2} (\text{First Term} + \text{Last Term})\]
n is the number of terms of a sequence

Answer 56

\[\frac{n}{2}(first term+last term)=n \frac{first term+last term}{2}\]

Answer 57

same thing

Answer 58

ok

Answer 59

so the 20/2(5+100)
10(105)
1050?

Answer 60

yes

Answer 61

YAY! i learned something new! thank you!

Answer 62

n in this particular sequence of 5, 10, 15 ... 100 is

100 = 5 + (n-1)5
95 = (n-1)5
19 + 1 = n => n =20

apply the formula

\[\S_{20} = \frac{20}{2}* (5 + 100) = \frac{5 + 100}{2}\times 20\]

Answer 63

i see tht bhaiya i understnad it now