Question

Find the sum 6+9+12+...+93Sn=

Answer 1

We notice that:
9-6 = 3
12-9 = 3 , Then we can conclude that this is an arithmetic progression with:
1st term a₁ = 6 and with common difference d = 3

So the first term is 6 and the last term is 93.
the formula of the sum in a A.P is :

S = (a + last term).n/2, n being the rank of the last term. So to be
able to find S, we have to calculate the value of n

We know that the last value of a A.P is :
last value = a₁ + (n-1)d
93 = 6 +(n-1)(3) → 93 = 6 + 3n -3 → n = 90/3 → n = 30 (rank 30th)

Now we can find the sum:
S = (a₁ + last term)n/2

S = (6+93)30/2

S = (99).15 = 1,485