The third term of an A.P. is 7 and the seventh term exceeds three times the third term by 2. Find the first term, the common difference and the sum of first 20 terms.
a3 = 7
a + 2d = 7 (i)
a7 = 3a3 + 2
a + 6d = 3(7) + 2
7 – 2d +6d = 21 + 2
4d = 16
D = 4
From (i), a = 7 – 2(4)
= -1
S20 = [2(-1) + (20 – 1)4]
= 10 [-2 + 76]
= 740