Question

When finding the sum of the arithmetic series 4 + 1 + -2 + -5 + -8 + -11, you will have a step of work that contains the number -3. Use complete sentences to describe how the -3 was calculated and what it means.

Answer 1

Please use a bracket for writing +(-2)

Answer 2

oh I'm sorry, the problem was written like that. I'll fix it! :) sryy

Answer 3

No need... Its good to see that you understand that :)

Answer 4

yes thank you for letting me know that! :)

Answer 5

Can you guess what is -3 here ?

It is common difference of this AP

Answer 6

oh ok. So I Will be using the same formula?

Answer 7

Yep

Answer 8

okay, how do I find a_1?

Answer 9

a_1 is the first term of the AP. What is the first term here ?

Answer 10

4 is the first term

Answer 11

So it is a_1

Answer 12

so a_1=4....do I need to add all of them to get that total?

Answer 13

No use the formula for sum of an AP

Answer 14

\[\large{S_n = \cfrac{n}{2}[2a+(n-1)d]}\]

Answer 15

n = number of terms in the AP (Count them)
d = You calculated before = -3
a = a_1 = first term = 4
S_n = sum the question wants

Answer 16

okay so
n=6
d=need to find
a=4
S_n= (do I add them)

Answer 17

n - correct
d = a_2 - a_1 = second term - first term
a = 4
S_n = Use the formula to calculate it

Answer 18

ohhhh okay, sry about that! I will calculate a let ya know in a sec... thank you in advance for your help!! :)

Answer 19

Your welcome (in advance) :D

Answer 20

;) :D

Answer 21

-117

Answer 22

Although they want you to use the formula to calculate the arithmetic sum, with just six terms it is so much easier to simply add the 6 terms which can be done mentally while reading the problem!

Answer 23

How ?

Answer 24

@superhelp101 how ?

Answer 25

well I used the formula and just plugged in....@vishweshshrimali5 maybe I made an error...let me redo

Answer 26

d = -3

Thus:

\[\large{S_n = 6/2(2*4 + (6-1)*(-3))}\]

\[\large{\implies S_n = 3*(8 - 15)}\]

\[\large{\implies S_n = -21}\]

Answer 27

oh yes....sry just looked back and that's what I got. What was aum taking about?

Answer 28

He was saying that since the number of terms (n) is small we can easily add up the terms. :)

This method can be used to check the answer

Answer 29

oh ok

Answer 30

Also you can use this method if it is a multiple choice question. But, if it is a subjective question then don't use it :)

Answer 31

kk :)

Answer 32

so the sum is -21. And now I need to add them again?

Answer 33

No

Answer 34

Just to double check your answer:
The 4 + 1 cancels with -5 leaving you with -2 - 8 - 11 = -21

Answer 35

Add them and see if you get the same answer

Answer 36

ohhhhh I see makes sense! :)

Answer 37

What @aum is using a very intelligent method of solving the questions. But I would suggest you to use it ONLY when you have practised a large number of questions. After solving lot of questions, these type of things come in habit :)

Answer 38

okay, thank you for the tip! :) and thank you @aum for introducing it to me!

Answer 39

If you would notice, he very smartly observed that 4+1 = 5 and there is another -5 which would cancel out each other, leaving us only with 3 terms to add which is much easier than adding 6 terms.

Answer 40

yes, I see.. :)