How many terms of the arithmetic sequence 2,4,6,8, ... add up to 60,762?

Question

parthkohli · Answer

$ \color{Black}{\Rightarrow S = {n \over 2}(1st + last) }$

anonymous · Answer

The sum of integers from 1 to n equals n(n+1)/2.
The sequence given is 2 times the sum from 1 to n.  So our equation is:
30,381 = n(n+1)/2

anonymous · Answer

not much new here, sorry

anonymous · Answer

How do I use that when I don't have n?

lgbasallote · Answer

first find a_n

$$a_n = a_1 + (n+1)d$$
$$a_n = 2 + (n-1)2$$
$$a_n = 2 + 2n - 2$$
$$a_n = 2n$$
now use the formula for sum
$$s_n = \frac{n(a_1 + a_n)}{2}$$
$$60762 = \frac{n(2 + 2n)}{2}$$
$$60762 = \frac{2n+2n^2}{2}$$
$$60762 = n + n^2$$
$$n^2 + n - 6072 = 0$$
now use $$n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

lgbasallote · Answer

uhh that should be $$n^2 + n - 60762 = 0$$

then use quadratic formula..you'll get your answer ;)

lgbasallote · Answer

do you get it @derptastic878 ?

anonymous · Answer

Yes, thanks. Just trying to work out a number so big, haha.

lgbasallote · Answer

hehe

anonymous · Answer

Also I put in the wrong number and didn't notice it was a perfect root. x_x