In an arithmetic sequence the fifth term is 34 and the tenth term is 43 find the first term and the sum of the first 20 terms of the sequence

5th term =     a1 + 4d = 34
10th term =   a1 + 9d = 43

subtracting first equation from the second gives:-
  5d = 9 so d = 9/5  or 1.8

first term  a1 =   34 - 4(1.8) =  26.8

Sum of first 20 terms  = (20/2)[2(26.8) + 19*1.8]
                                   = 10* 87.8
                                   = 878

The answer is that the rate of change is $50 per 1 monthhope this ; )