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