Question

Question #86a89

Answer 1

The answer is 2) 4.

Explanation:

You can see that ach term increases by one. This is characteristic to an arithmetic series. To save you from adding 80 numbers on your calculator 4 times, there is a formula that finds the sum of all of these numbers.

`S = n/2(a_1+a_n)`

`S` is the sum of this large number, `n` is the number of terms you will have, `a_1` is the first term, and `a_n` will be the final term.

Now that we have this, we can plug it in to our expression.

`n` will be 81, because we have 81 terms going up from `(n+20)` to `(n+100)`, counting `(n+20)`.

(not to be confused with the n in your problem)

`a_1` will be (n+20), of which we will use trial and error with each number.
`a_n` will be `(n+100)`, the last term in this sequence

Now that we can plug this in, and I will do the math on this part.

With 1, the answer is 4941, which is not a perfect square
With 4, it is 5184 which WORKS!! (the square root is 72)
We can stop there, as it is the smallest number listed that is a perfect square (9 and 16 are larger of course).
There it is, 4 is the right answer.
Good luck!