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Arithmetic progression

So I have question where the first term is 28 and increases by 3 for every term afterwards. There is a known total of 17000, how many terms until we get to that total. Please help

Reply 1

Muttley79

Original post by Hobble20

So I have question where the first term is 28 and increases by 3 for every term afterwards. There is a known total of 17000, how many terms until we get to that total. Please help

I would use the sum of a series formula and set it equal to 17 000 then solve. Post your working if you get stuck.

Reply 2

Hobble20

hi is stuck trying to work out how to redo the formula I’ve posted, if you can help it would be much appreciated

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Reply 3

the bear

Original post by Hobble20

hi is stuck trying to work out how to redo the formula I’ve posted, if you can help it would be much appreciated

so you have the right formula.... you have values

S_n = 17000

a = 28

d = 3

put these in then you can work out n

Reply 4

Muttley79

Original post by Hobble20

hi is stuck trying to work out how to redo the formula I’ve posted, if you can help it would be much appreciated

Sorry - you need to use reply to quote me so I know you've responded.

Have you substituted in a = 28, d = 3 and sum = 17 000 - your photo only shows the formula

Reply 5

Hobble20

Original post by Muttley79

Sorry - you need to use reply to quote me so I know you've responded.

Have you substituted in a = 28, d = 3 and sum = 17 000 - your photo only shows the formula

Hi please forgive me, I’m new to this site as a user, please see photo

image.jpg506.5KB

Reply 6

Muttley79

Original post by Hobble20

Hi please forgive me, I’m new to this site as a user, please see photo

Great - now expand and tidy up, post what you get :smile:

Reply 7

Hobble20

Original post by Muttley79

Great - now expand and tidy up, post what you get :smile:

Right this is where I get stuck, not sure how to alter the formula to get the value for “n”

image.jpg489.1KB

Reply 8

Muttley79

Original post by Hobble20

Right this is where I get stuck, not sure how to alter the formula to get the value for “n”

OK can you expand and collect like terms?

Reply 9

ghostwalker

Original post by Hobble20

Right this is where I get stuck, not sure how to alter the formula to get the value for “n”

As Muttley79 said, expand and tidy up. Because you're going to have a term in n^2 there, making n the subject although doable isn't necessarily the way to go. You will have a quadratic in n, and use what ever means you've been taught to solve it.

HOWEVER, unless I made a slip, there is an error in the question. You cannot get a total of 17000 exactly. Please check the original question. I suspect it should say 170.