Sum of n Terms: Pair Them Up
S_n = n/2 * (2a + (n-1)d) — the formula falls out of pairing first and last terms.
Equation
y = x/2*(2*1+(x-1)*1)
Graph
Table
| x | y |
|---|---|
| 1 | 1 |
| 2 | 3 |
| 3 | 6 |
| 4 | 10 |
| 5 | 15 |
| 6 | 21 |
| 7 | 28 |
| 8 | 36 |
| 9 | 45 |
| 10 | 55 |
What this lesson covers
What you do
You shape the function y = x/2*(2*a+(x-1)*d) and watch the graph answer.
Challenges to clear
- Set a = 3 and d = 5: the sum of the first 10 terms is 255 — pair first with last and count the pairs.
- S_1 is just the first term: x = 1 shows 3.
- Start the sum from a first term of 2 — slide a there.
- Now the step: the first 8 terms must total 100. Pair the first with the last and count the pairs.
Check yourself
In the formula S_n = n/2 * (2a + (n-1)d), what does the term (n-1)d represent?
- The difference between the first and last term — correct
- The product of n and d
- The average of n and d
- The middle term of the AP
Think about it
- S_n = n/2 · (2a + (n−1)d). With a = 3, d = 5: what is S_10?