Question

the n th term of series-3+6-12+24-48+..... is

Answer 1

let us look at your sequence 3, 6, 12, etc.

each term has the common factor of 3 i.e. we have the sequence

3*1, 3*2, 3*4, 3*8, 3*16, 3*32....

ignoring the 3's for a moment, the sequence is

1, 2, 4, 8, 16, 32...

these are all powers of two

i.e. 2%5E0=1 2%5E1=2 2%5E2=4etc

The powers of 2 are 1 less than the position of the number in the sequence

so we can now say

the sequence is

3%2A2%5E%28n-1%29