Hi Joey,

Let's try this one

Find the sum of the first 123 terms of 5, 3, 4, 2, 5, 3, 4, 2,... What yo need to see here is that the sequence repeats after 4 terms 5, 3, 4, 2. How many times does this pattern repeat in 123 terms? 123/4 = 30 with a remainder of 3 and hence the pattern 5, 3, 4, 2 repeats 30 times and then there are 3 more terms to complete the sequence. The last three terms are 5, 3, 4. Thus the sum of the 123 terms is

30(5 + 3 + 4 + 2) + 5 + 3 + 4 = 30(14) + 12 = 420 + 12 = 432.

I hope this helps,
Penny