How do you determine the sum of the first twenty terms of the sequence whose first five terms are 5, 14, 23, 32, and 41?
1 Answer
1810
Explanation:
There are two things we can discern from looking at the sequence:
1) we can see that each term is the previous term plus nine.
2) when we cut this sequence in two, all the pairs, counting up and down from the middle have the same sum (ex: if we take the first 4 numbers, 14+23=5+32, so the sum of the first 4 is equal to twice the sum of the second and the third)
The first observation gives us the generic formula for a term in relation to it's position
With that, coupled with the second observation, we can see that if we calculate what is the 10th and the 11th terms and add them, we will have a value that is the same for all 10 pairs of numbers (10th & 11th, 9th and 12th, 8th and 13th, and so on). So we take that one sum and multiply by 10 to get our result.
so:
