Question

The sum of nine consecutive integers; n = first integer of the nine

Answer 1

If n is the first, then what does the ninth term look like?

Answer 2

not sure

Answer 3

They are consecutive integers, so they come one right after the last.

Answer 4

i know for if its the 8 term the answer would be 8n+28

Answer 5

(In the language of arithmetic sequences, the common difference is 1).

Answer 6

consecutive integers are n , n+1, N+2

Answer 7

Well, there's only nine of them, so let's list them all out and look, eh?

n, n+1, n+2, n+3, n+4, n+5, n+6, n+7, n+8

Answer 8

yeah

Answer 9

So there are nine n's and the series 1+2+3+4+5+6+7+8.

Answer 10

Notice in the series, 1+2+...+8 that the first and last terms add up to the same number, 9, that the second and second-to-last add up to, and so on.

Answer 11

So there are four pairs of numbers that add up to 9.

Answer 12

like 4 and 5?

Answer 13

Those too, yep.

Answer 14

how would the equation look like for this question?

Answer 15

Well, like we saw, there are 9n and 4 groups of 9 make 36, so S=9n+36

Answer 16

oh i see

Answer 17

thanks

Answer 18

No prob'
Try a couple more similar examples and think through the reasoning that I showed you until you see how it all fits together.

Answer 19

yes i shall do that