arggh series (1 Viewer)

[joannee--]

hey sorry i have another series question ..


the sum of the first 5 terms of an arithmetic series is 110 and the sum of the first 10 terms is 320. Find the first term and the common difference.






thankss ..

 

[watatank]

the sum of the first 5 terms of an arithmetic series is 110 and the sum of the first 10 terms is 320. Find the first term and the common difference.

Sn = (n/2) * [2a + (n-1)d ]

S(5) = (5/2) * (2a + 4d) = 110

10a + 20d = 220 .................. (equation 1)

S(10) = (10/2) * (2a + 9d) = 320

20a + 90d = 640 .................. (equation 2)

solve equation 1 and 2 simultaneously

EDIT: because im bored il finish it off

10a + 20d = 220 .................. (equation 1)

2 * (equation 1) ----> 20a + 40d = 440 .................. (equation 3)
20a + 90d = 640 .................. (equation 2)

equation 2-equation 3: 50d = 200 ... d = 4

sub back into equation 1

10a + 80 = 220

10a = 140.... a = 14

 

[bos1234]

hsc 2004???????????