Final answer:
The partial sum S₅ of the geometric sequence with a = 5, r = 2, and n = 5 is calculated using the formula for the sum of the first n terms of a geometric sequence, giving a result of 155.
Explanation:
To find the partial sum S₅ of a geometric sequence with the given conditions: a = 5, r = 2, and n = 5, we can use the formula for the sum of the first n terms of a geometric sequence, which is Sᵢ = a(1 - r⁻⁵) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms.
Plugging in the values, we have: Sᵢ = 5(1 - 2⁻⁵) / (1 - 2) = 5(1 - 32) / (-1) = 5 * 31 = 155.
Therefore, the partial sum S₅ of the sequence is 155.
