The third term of an A.P is 10 and the sixth term is 43 find: the sum of the first 20 terms with shown working
The common difference of the A.P is given by
d = (43 - 10)/(6 - 3) = 33/3 = 11
The nth term of the A.P is given by
a_n = a_1 + (n - 1)d
The first term of the A.P is given by
a_1 = 10 - (3 - 1)11 = -2
The sum of the first 20 terms is given by
S_20 = (20/2)[2a_1 + (20 - 1)d]
S_20 = (20/2)[2(-2) + (20 - 1)11]
S_20 = (20/2)[-40 + 209]
S_20 = (20/2)[169]
S_20 = 840