1. Sum of first 5 terms = 62
2. Sum of first 4 terms = 54
3. Sum of first 3 terms = -15
Sum of Arithmetic sequence
From the question, we are to evaluate the sum of the given sequence
1. Sum of the first 5 terms of the sequence ai = 2^i
ai = 2^i
a1 = 2¹ = 2
a2 = 2² = 4
a3 = 2³ = 8
a4 = 2⁴ = 16
a5 = 2⁵ = 32
Sum of first 5 terms = 2 + 4 + 8 + 16 + 32
Sum of first 5 terms = 62
2. Sum of the first 4 terms of the sequence ai = (i + 1)²
ai = (i + 1)²
a1 = (1 + 1)² = 2² = 4
a2 = (2 + 1)² = 3² = 9
a3 = (3 + 1)² = 4² = 16
a4 = (4 + 1)² = 5² = 25
Sum of first 4 terms = 4 + 9 + 16 + 25
Sum of first 4 terms = 54
3. Sum of the first 3 terms of the sequence ai = (1 - 3i)
ai = (1 - 3i)
a1 = (1 - 3(1)) = 1 - 3 = -2
a2 = (1 - 3(2)) = 1 - 6 = -5
a3 = (1 - 3(3)) = 1 - 9 = -8
Sum of first 3 terms = -2 + -5 + -8
Sum of first 3 terms = -2 - 5 -8
Sum of first 3 terms = -15
Hence,
1. Sum of first 5 terms = 62
2. Sum of first 4 terms = 54
3. Sum of first 3 terms = -15
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