What is the formula for the sum of an arithmetic sequence?
2 Answers
# S_n = n/2(2a+(n-1)d) #
Explanation:
Suppose we have an AP with first term
# S_n = a + (a+d) + (a+2d) + ... + (a+(n-1)d) #
Writing the same sum, but in reverse, we get:
# S_n = (a+(n-1)d) + ... (a+2d) + (a+d) + a #
If we add both of these we get:
# 2S_n = (2a+(n-1)d) + (2a+(n-1)d) + ... + (2a+(n-1)d) #
# \ \ \ \ \ = n(2a+(n-1)d) #
Leading to the standard AP summation formula
# S_n = n/2(2a+(n-1)d) #
The sum of an arithmetic sequence is given by
Explanation:
Let
Adding up the two equations term by term we get
*Notice how the
Since we have