Page 18 - Math SL HB Sem 1

Stso CE ANI) SERIES

AItI'IHMT]1'I (] SERIES

If S, is the sum of the first r? terms of an Ap with last term l, then
Sn: u, *(u,+d)+(arr+2d)+...+(/-d) + / (l)

reversing S" 1 + (/-d) + (l -2d) +.. + z, *d)+ 7, (2)
(

adding 25,: (2, +f + (u,+[) + (a, +I) + ... + (2,+I) + (u,+l)

as there are n terms we have

n
2S,,= n(u,+l) i.e S, (u, + l) ... formula I
2

-
Also, because the n'r term, /, is z, + (n l)d, we have
Sr= ! { u.,'t ur+ (n-l )d }

t1
)
l2u,+ 1n -l d ) ... formula 2
2

Either ofthese lormulae can be used to find the sum ofthe first n terms of an Ap
NOTE:
4, -E -s, ,
'l'he
Example I : tenth term ofan arithmetic sequence is 63 and the sum of the first 20

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

2-6