Page 18 - Math SL HB Sem 1

SEO CE ANI) ERIES

ARII'IIMETIC SERIES

If S, is thc sum of the first n terms of an Ap with last term I then
Sn: u, t(u, + d)+(zr+2d)+...+(/-d) + / (l)

reversing Sn= l+ I + -2d +.. + a, *d)+ 1, (2)

adding 25,=(u, +I) + (u,+t) + (u,+l) +... +(u,+I) + (u,+t)

as there are n terms we have

n
2Sn= n(2,+/) i.e Sn (u.t + l) ... formula I
2

Also, because the n'' term, /, is z, + (n l)d, we have
n
S +(n-l)d)
,\\+a,
n
l2u,+(n-l)d) ... formula 2
2

Either olthese formulae can be used to find the sum ofthe first n terms ofan AP
NOTE: 4, -E, q-,

Example I: The tenth term olan arithmetic sequence is 63 and the sum oithe first 20

terms is six times the sum of the first ten terms. Find the first term and its
common difference.

2-6