C2 arithmetic progression question

A) the sum of the first ten terms of an AP series is 115. the sum of the next four terms of this series is 130. find the first term and the common difference of the AP.

from this i got S10 = 115 so

S10 = 10/2 (2a + 9d)
S10 = 10a + 45d

and then the next four terms, i dont even know how to begin.

\displaystyle \sum_{r=11}^{14} u_r= \sum_{r=1}^{14} u_r - \sum_{r=1}^{10} u_r

Reply 2

TSR George

OP

17

Original post by RDKGames

\displaystyle \sum_{r=11}^{14} u_r= \sum_{r=1}^{14} u_r - \sum_{r=1}^{10} u_r

i havent gone to learn the summits yet, so that looks new for me. is there like a different way using just sums of n, simultaneous equations, nth term and whatnot?

i dont mind if its longer.

Your sequence isn't defined so you'd have to split the summation into 2 parts as I have shown above.

All it says is that the summation of "the next 4 terms" is equal to the summation from the first to the 14th term, then take away the summation of the first 10 terms which you already found.

Reply 4

TSR George

OP

17

Original post by RDKGames

Your sequence isn't defined so you'd have to split the summation into 2 parts as I have shown above.

All it says is that the summation of "the next 4 terms" is equal to the summation from the first to the 14th term, then take away the summation of the first 10 terms which you already found.

ah okie thanks

Reply 5

an_atheist

15

That looks good, now if the next four terms add to 130 what do the first 14 terms add to? Then repeat what you did for the first 10 and yo should have 2 simultaneous equations to solve.

Just realised you can also say

S_{14}=115+130

as well and get simultaneous equations that way

My brain doesn't work well today :frown:

Reply 7

TSR George

OP

17

Original post by RDKGames

Just realised you can also say

S_{14}=115+130

as well and get simultaneous equations that way

My brain doesn't work well today :frown:

but i can also work it out the way u initially did it right?

Original post by an_atheist

That looks good, now if the next four terms add to 130 what do the first 14 terms add to? Then repeat what you did for the first 10 and yo should have 2 simultaneous equations to solve.