The first term of the geometric sequence is equal to 5.
A geometric sequence or progression is a sequence where every term bears a constant ratio to its preceding term. The nth term of a geometric sequence is calculated as ar⁽ⁿ ⁻ ¹⁾ where a is the first term and r is the common ratio.
Given the common ratio r = 4 and the 6th term a₆ = 5120, we can derive the first term a as follows:
a4⁽⁶ ⁻ ¹⁾ = 5120
a4⁵ = 5120
a1024 = 5120
divide through by 1024
a = 5120/1024
a = 5.
Therefore, the first term of the geometric series is calculated to be a = 5.