Answer: Choice A) 663
=========================================================
Step-by-step explanation:
Notice that each term
appears exactly twice in all of the sums mentioned
a₁+a₂=1, a₂+a₃=2, a₃+a₄=3, a₄+a₅=4,....a₅₀+a₅₁=50 and a₅₁+a₁=51
What we can do is add up the left hand sides of those sums, separate from the right hand sides
L = sum of the left hand sides

R = sum of the right hand sides

To compute the value of R, I used the formula

-----------------------------
After establishing L and R, we equate the items and divide both sides by two like so:

This points us to choice A as the final answer.