Question

what is the sum of a 14-term arithmetic sequence where the last term is 30 and the common difference is -5?

Answer 1

do you want me to like show my work? or do you just want the answer?

Answer 2

work please!

Answer 3

ok so the arithmetic sequence equation is: a_n=a_1 + (n-1)d

Answer 4

okay

Answer 5

since you dont have the first term to plug into the equation you plug what you have in and solve for a_1 first what do you get?

Answer 6

after you get the a_1 then you can use the arithmetic Series equation: s_n =n/2[2a_1+(n-1)d] to find the sum

Answer 7

so a_n=30
n=14
d=-5

Answer 8

30=a_1+ (14-1)-5
30=a_1+(13)-5
30=a_1+(-65)
30=a_1-65
95=a_1

Answer 9

So since you have a_1 now you plug it into the arithmetic series equation to find the sum

Answer 10

so
S_n=14/2[2(95)+(14+1)-5]
S_n=7[190+(15)-5]
S_n=190-75
S_n=115

Answer 11

So the answer is 115

Answer 12

Do you understand it?

Answer 13

no still confused
the answers is either:
875
812.5
455
422.5

Answer 14

Is the problem right that you typed? cause i did my math right so is anything different?

Answer 15

if the common difference is not negative it will be very different

Answer 16

the question is written right, i'm confused because i got the same answer you did.
but 115 isn't one of the answers i can choose from ?

Answer 17

Hmm. thats odd :l none of the answers can be "none of the above"?

Answer 18

no those are the only ones i can choose.

Answer 19

ok hold on a second ill do my math again 805 an answer?

Answer 20

no

Answer 21

its 875
if you use the other equation for the sum : S_n=n/2(a_1+a_n)
S_n=14/2(95+30)
S_n=7(125)
S_n=875

Answer 22

okay, thank you so much!

Answer 23

No problem! lol