how do you solve it?

Question

10+12+14+.....+x=306 x=?

Answer 1

first you add the numbers together. in this case they would equal 36. then you subtract it from both sides. this leaves just x on one side and 270 on the other. x=270.

Answer 2

10+12+14+.....+x = 306
LHS is a arithmetic progression. so sum is given by
S = x/2 * (2a + (x -1)d)
where d = difference between two consecutive numbers
In our case d = 12 -10 = 2
so S = x/2*(2*10 + (x -1)*2) = 306
or x(20 + 2x -2) = 306*2
or 2x^2 + 18x - 612 = 0
or x^2 + 9x - 306 = 0

Answer 3

There is no value of x that will provide a sum of 306.
x = 34 gives a sum of 286 and x = 36 gives a sum of 322.

You must have error in writing this arithmetic series problem.

Answer 4

x is probably 20, but I wouldn't bet on it.
One technique, when all else fails, is to sneak up on it.
It certainly looks like this is an arithmetic progression,
with 10 the first term and a difference of 2. Assuming this pattern continues, we get
Term.......Value.....total
Position................value
-----------..---------..----------
1...............10.........10
2................12.........22
3...............14..........36
4................16.........52
5................18.........70
6................20.........90
7................22........112
8................24........136
9................26........162
10..............28........190
11..............30........220
12..............32........252
14..............34........286

The next term is the "x" term. To add to 306, the value has to be 20.
To follow the arithmetic progression, the next value,
the 15th term, and the "x" term, should be 36.
There is no integer that works, IF this is truly an arithmetic series.
I' m going to keep an eye on the answers you get.
Maybe I'm missing something.