If the first, second and last term of an A.P. are and respectively. then its sum is
Explanation for the correct option
Step 1: Solve for the number of terms in the given progression
Given that, first, second and last term of an A.P. are and respectively
Let be the common difference between two successive terms of the arithmetic progression
are successive terms in the A.P then
The term of the A.P is given as where is the first term and is the number of terms in the A.P
Consider the term to be the last term of the A.P. Substituting all the required values we get,
Step 2: Solve for the sum
The sum of terms of an A.P is given as
Substituting all the required values we get
[from ]
Thus the sum of all the terms of the given A.P is .
Hence option(C) i.e. is the correct answer.