Question

What is the sum of a 12-term arithmetic sequence where the last term is 13 and the common difference is -10?

A. 605
B. 660
C. 748
D. 816

Please don't just give me the answer, I want to know how to do it. I can't figure it out.

Answer 1

12th term = a1 + 11d

where a1 = first term and d = common difference -10
so we have
13 = a1 -11*-10

solve for a1

then find the sum using the formula

Sn = (n/2) [ a1 + L] where L = last term

Answer 2

Use the explicit formula to find \[a _{1}\] then use the formula below to find the sum
\[S _{n} = n(\frac{ a _{1}+a _{n} }{ 2 })\]

Answer 3

nth term of an AS = a1 + (n - 1)d

Answer 4

So what is L?

Answer 5

L = 13 as given

Answer 6

I overlooked that. I apologize.

Answer 7

thats ok

Answer 8

So we have 13 = a1 -11*-10.
Do i subtract 11?

Answer 9

or add*

Answer 10

no do the multiplication first

Answer 11

13 = a1 + 110

Answer 12

oh okay. so 13=a1+110? since it was two negatives?

Answer 13

right

Answer 14

okay then subtract 110 from 13 right?

Answer 15

yes

Answer 16

a1=-97

Answer 17

right
now use the formula for sum of n terms

Answer 18

n = number of terms in the As which is 12

Answer 19

Sn = (n/2) [ a1 + L] so S(12)= (12/2) (-97+13) ?

Answer 20

right

Answer 21

S12=(6)(-84)

Answer 22

sujuex's formula is same as mine but written in different way

Answer 23

It looked about the same but just more confusing kind of.

Answer 24

I got -504 but that isn't one of the choices. :(

Answer 25

you wont get one of the options as an answer
I know Maybe you havent go the question right

Answer 26

maybe d = 10 ?

Answer 27

it's from Fvls so i don't know. :/

Answer 28

i could try that.

Answer 29

the equation that is in my lesson is Sn =  [2a1 + (n – 1)d] could i try to plug them in here?

Answer 30

sorry - thers a mistake

Answer 31

13 = a1 +1*-10 - not a double minus

Answer 32

ohhh okay.
13=a1+(-10)

Answer 33

so 13 = a1 - 11*10
and a1 = 123

Answer 34

okay so S12 = (12/2) [ 123 + 13]

Answer 35

yea

Answer 36

6*136=816

Answer 37

right

Answer 38

Yay! thank you so much. And i am so sorry to ask this but could you guide me through another? i think i've got it down but could you tell me if i got it right?

Answer 39

ok I've got 10 minutes then i must go

Answer 40

What is the common difference of a 43-term arithmetic sequence where the first term is -13 and the sum is 9,374?
A. 11
B. 11.5
C. 12
D. 12.5

Answer 41

Thank you so much.

Answer 42

would i use the same equation?

Answer 43

you know the sum of n terms and n = 43 and you also know a1 so use the formula

Sn = (n/2)[2a1 + (n - 1)d]

9374 = (43/2) [2*-13 + (43-1)d]

9374 = 21.5[ -26 + 42d]

solve this to find value of d

Answer 44

would i add -26 and 42?

Answer 45

or subtract 21.5 from 9374?
if so 9352.5=(-26+42d) right?

Answer 46

no - remember when you have a mixture of adds and multiplies you do the multiply first. In any case you cannot add unlike terms . 26 and 42d are unlike terms.
in this case you have the brackets so you multiply first the -26 then the + 42d by 21.5

use ur calculator.

then solving for d is easy

sorry gotta go

Answer 47

oh okay. uhm
9374= -559 + 903d

Answer 48

9374= -559 + 903d
add 559
divide by 903
and the answer is 11.
THANK YOU! I could just hug you. I know you're gone but yo're wonderful thanks so much.