The rth term of an arithmetic series is (2r – 5). Show that \sum_{r = 1}^{n} (2r - 5) = n(n – 4).

Step 1: To find the 1st term, plug in n = 1. in the sequence and simplify
[NOTE: Knowing that, n represents the position of a term in the sequence. So change the n values.]
Step 2: To find the 2nd term, plug in n = 2. In the sequence and simplify
Step 3: Take the various n values and substitute in the sequence, till you get the required sequence.
Step 4: Find the sum of the series.
Skill i: Identify the first term in the sequence, call this number a.
Skill ii: Calculate the common difference(d) of the sequence.
Skill iii: Identify the number of terms (n).
EXAMPLE: In A.P 2, 4, 6,..... find the sum of the first 10 terms. So take n=10
Skill iv: Plug the values of n, d, and a into the formula.
[FORMULA: The formula for finding the sum of first n terms of an
arithmetic sequence (S_n) =(n/2)[2a + (n- 1)d]
Skill v: Simplify further..(Apply the BODMAS rules)
Skill vi: Verify that the result is equating the given answer or not