What is S_(10) for 1+4+16+64+...?
The given sequence is a geometric sequence with first term 1 and common ratio 4.
So, the 10th term is given by:
S_10 = 1*(4^(10-1)) = 1*(4^9)
S_10 = 262144
Therefore, S_(10) for the given sequence is 262144.
are you sure
I apologize for the mistake, I misread the question. The question is asking for the sum of the first 10 terms of the given sequence.
The given sequence is 1, 4, 16, 64, ... which is a geometric sequence with first term 1 and common ratio 4.
The sum of the first 10 terms is given by:
S_10 = (1 - 4^10)/(1-4)
S_10 = (1 - 1048576) / (-3)
S_10 = 1048575 / 3
S_10 ≈ 349525
Therefore, S_(10) for the given sequence is approximately 349525.
are you sure thats correct
I apologize for the mistake again. The correct sum of the first 10 terms of the given sequence is:
1 + 4 + 16 + 64 + 256 + 1024 + 4096 + 16384 + 65536 + 262144 = 349525
Therefore, the sum S_(10) for the given sequence is indeed 349525.