solve for x and then find t1, t2, t4. then find S15?

Question

given that the 1st, 2nd, and 4th terms of an arithmetic sequence are 11-x, 2x+1 and 3x+1 respectively: solve for x and then find t1, t2, t4 and then find S15

Answer 1

t2 - t1 = (2x + 1) - (11 - x) = 3x - 10. This is the common difference d. Since t2 + 2d = t4, we have (2x + 1) + 2(3x - 10) = 3x + 1; this tells us that x = 4. Therefore the terms are 7, 9, 11, 13, .... We also have d = 3x - 10 = 2, so now you should be able to find S15.