Question

Solve the series 4,6,8,10,20,-6,70,30,350,-34,2450,?

Answer 1

It's really riddle series. I took 5 minutes to solve it.
Let's try to give you explanation ,

given 4, 6, 8, 10, 20, -6, 70, 30, 350, -34, 2450, ?
It seems irregular form .but when you see deeply you observed this is combination of two different series.
see 1st, 3rd, 5th , 7th ,9th , 11th places of series.
e.g., 4, 8, 20, 350, 2450
Here I observed ,
4 × 2 = 8
8 × 2.5 = 20
20 × 3.5 = 70
70 × 5 = 350
350 × 7 = 2450
If you see deeply you observed :
2 + 1 × 0.5 = 2.5
2.5 + 2 × 0.5 = 3.5
3.5 + 3 × 0.5 = 5
5 + 4 × 0.5 = 7
So, next clue must be 7 + 5 × 0.5 = 7 + 2.5 = 9.5
so, finding 13th terms , multiple 9.5 with 12th term

Now, 2nd series.
see , 2nd , 4th , 6th , 8th , 10th places of given series.
e.g., 6, 10, -6, 30, -34
let's try to see relation .
|6 - 10| = 4 = 2²
|10 -(-6)| = 16 = 4²
|-6 -30| = 36 = 6²
|30 -(-34)| = 64² = 8²
So, 12t term must be in such a way that , difference between 11th and 12th = 10²
Hence, Let 12th term is x
Then, |x -(-34)| = 100
x + 34 = 100
x = 66

Hence, next term is 66
So, the final series , 4, 6, 8, 10, 20,-6,70,30,350,-34,2450, 66