math help!
posted by Riana on .
the 10th term is 34 of arithmetic series and the sum of the 20th term is 710 i.e S20=710.what is the 25th term?

Let a = first term, T1
Let b = Tn+1  Tn = term difference
a + 9b = 34
S20 = T1 + T2 + ...T19 + T20
= a + (a+b) + (a+2b) + ...(1+19b)
20a + (b)(1+2+3+...19)
= 20 a + 190 b = 710
20a + 180b = 680
10 b = 30
b = 3
a = 34 27 = 7
Arithmetic Series is
7, 10, 13, 16, 19, 22, 25, 28, 31, 34,...
10th term = 34
Check the sum of the first 20 terms and predict the 25th