number sequences....

[bumblebee123]

I would 1st list the sequence you want then try to figure out how to sum them. The sequence is 12, 15, 18, ... , 99
Now that you know the sequence get to work!

so the sequence is 9 + 3n?

 

[Steven G]

so the sequence is 9 + 3n?

I'd prefer that you say a_n = 9 + 3n

The real things you need are a₁, d (both of which I am sure you know) and the term number for 99. And 99 is no longer the 90th term!

 

[bumblebee123]

a1 = 9 + ( 3 x 1) = 12

d = 3

term number for 99: n = 30

 

[bumblebee123]

here's what I did to answer (c) :

the sum of all 2-digit numbers which are multiples of 3 =

S30 = 30/2 [ (2 x 12 ) + ( 30-1 )3 ]
S30 = 15 [ 24 + ( 29 x 3 ) ]
S30 = 15 x ( 24 + 87 )
S30 = 15 x 111 = 1665

therefore the sum of all 2-digit number which are not multiples of three = 4905 - 1665 = 3240 which is the correct answer