Question

sum of firsrt 5 terms of an arithmetic sequence is 45 what will be its third term

Answer 1

Sum of first 5 terms = 45
Sum of nth terms = 2(a + l)
Sum of 5th term = 2(a + 5)
45 = 2a+10
35 = 2a
a = 35/2
Sum of 5th terms = 1/2{2(35/2) + (5-1) d}
45 = 1/2(35 + 4d)
45 = 35/2 + 2d
45 -35/2 = 2d
(90-35)/2 =2d
55/2 = 2d
55/4 = d


a = 35/2
d = 55/4
n = 3
nth term = a + (n-1)d
3rd term =35/2 +(3-1)55/4
3rd term = 35/2 +110/4
3rd term = 35/2 + 55/2
3rd term = 90/2
3rd term = 45