arithmetic progression - An arithmetic series has first term a and common difference d. Prove that the sum of the first n terms of this series is \frac{n}{2}[2a + (n

Krishna (last edited 5 years ago) (Expert, Educator @Qalaxia)

Step 1: Write the Arithmetic Progression whose first term is a and common difference is d.

S = a + (a + d) + (a + 2d) + (a + 3d) + ……….. + {a + (n - 2)d} + {a + (n - 1)d} ……………….. (i)

Step 2: Write the terms of (Arithmetic Progression) S in the reverse order

S = {a + (n - 1)d} + {a + (n - 2)d} + {a + (n - 3)d} + ……….. + (a + 3d) + (a + 2d) + (a + d) + a..................(ii)

Step 3: Add the corresponding terms of two equations mentioned in step 1 and step 2

Step 4: Simplify further.