Question

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

Answer 1

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