Enter only the sum evaluate

Question

S₇for 5+10+20+40+....

Answer 1

You can see that this is a geometric series, because each term is double the one before it.

 

The sum of the first n terms of a geometric series is:

a₁ (1 - rⁿ) / (1 - r)

 

a₁ = the first term
r = the ratio between terms

 

You know that a₁ is 5.  And since each term is DOUBLE the one before, r must be 2.

 

So the sum is:

 

5 (1 - 2⁷) / (1 - 2) =

5 (1 - 128) / (-1) =

5 (-127) / (-1) =

635