What value should replace n in sigma notation to find the sum of the first 10 terms of the geometric sequence 1,1/4,1/16, . . . ?(1 point)
n=10
The sum of the first 10 terms of a geometric sequence can be calculated using the formula:
S_n = a(1 - r^n) / (1 - r)
where
a = first term of the sequence = 1
r = common ratio = 1/4
n = number of terms = 10
Plugging in the values:
S_10 = 1(1 - (1/4)^10) / (1 - (1/4))
S_10 = 1(1 - 1/1048576) / (3/4)
S_10 = (1 - 1/1048576) / (3/4)
S_10 = (1048575/1048576) * (4/3)
S_10 = 349525 / 262144
Therefore, the value of n to find the sum of the first 10 terms of the geometric sequence is 10.