Answers

2016-03-18T12:17:01+05:30
A.P: 103, 110, 117, ...., 999

a = 103  d = 7

n be the number of terms

 a_{n} = 999

103 + (n - 1)7 = 999

103 + 7n - 7 = 999

7n + 96 = 999

7n = 903

n = 129

Middle term =  \frac{n+1}{2} ^{th} term =  65^{th} = a + 64d = 103 + 64 x 7 = 551

 S_{n}  \frac{n}{2} [2a + (n - 1)d]

 S_{64}  \frac{64}{2} [2 x 103 + 63 x 7] = 20704

 S_{129}  \frac{129}{2} [2 x 103 + 128 x 7] = 71079

 S_{129} - ( S_{64} + 551) = 71079 - (20704 + 551) = 49824

Hope I helped you! :)
1 5 1