For the geometric series
1+ 4+ 16 + 64 + 256
what is the value of n?

n=5.

Step-by-step explanation:

The given geometric series is

1+ 4 +16 + 64 + 256

In the given G.P.  the number of terms is 5 and n represents the number of terms in a G.P. So, n=5.

Alternate method:

Here the first term is 1 and the common ratio is

The nth term of a G.P. is

where, a is first term and r is common ratio.

Substitute a=1, an=256 and r=4 in the above formula.

On comparing both sides we get

Add 1 on both sides.

Therefore, the value of n is 5.

$320 to $405

step by step explanation:

in one day he earns between $64 and $81

therefore if he works for 5 days, he will earn between 64 x 5 to 81 x 5

= $320 to $405