If , show that , from an arithmetic progression. Also find the sum of first terms.
Step 1: Find the terms of the given sequence
Given,
Substitute in given equation
Substitute in given equation
Substitute in given equation
Step 2: Identify the sequence as an arithmetic progression
As we can see form the given sequence.
A sequence is considered to be an arithmetic progression when the difference between two successive terms is constant.
Here the difference between two consecutive terms is
So, the given sequence is an arithmetic progression
Step 3: Find the sum of first terms
The sum of first terms of an arithmetic progression is given as
We have
Substituting these values in the standard result we get
Hence the sum of the first terms is .