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


7