Please help me with this sequence problem, I've tried several times!?

Question

Consider the sequences 5, 10, 20, 40, 80, ...
obviously each time it goes up by multiplying it by 2.
the question is to find S^20.

please help!
i think the formula is a^n(1-r^n)/(1-r)

Answer 1

The sequence is a geometric progression characterized by the starting value 'a' and the common ratio 'r'. The SUM of n terms, which is probably what you are looking for is then given by
S(n) = a(r^(n+1)-1)/(r-1) when r>0. If you are looking simply for the nth Term, this is given by T(n) = ar^n, n = 0,1,2,...

Answer 2

You mean find the 20th number in the SEQUENCE, or the sum of the SERIES when n=20? If you mean the sequence, then notice you can rewrite this as:
5, 5*2, 5*2*2, 5*2*2*2, or
5*(2^0), 5*(2^1), 5*(2^2), 5*(2^3),...

So the nth term is 5*(2^(n-1)). Thus the 20th term is 5*(2^19), or 2,621,440.

If you're talking about the sum of the SERIES, then you can use the forumla a(1 - r^(n+1)) / (1-r). So here a=5 and r=2. So the partial sum to n=32 is 5(1 - 2^(36))/(-1) = 5(2^36 - 1).

Answer 3

the given series is Geometric series with common ratio

r = 2 , first term a = 5 and n = 20
the formula to find the sum of first 20 terms is
Sn = a ( (r^n -1) / ( r - 1) ) .

S20 = 5 ( (5^20 -1 ) / ( 5 -1 ) )
= 5 ( 5^20 -1) / 4

Answer 4

1)an = 5*2^(n-1)
Sn= 5 (2^n-1) so
S_20 = 5((2^20-1)) =5,242,875

Answer 5

5(2)^19

Answer 6

ah yea its doubling innit eh