The nth term of a sequence is given by (-1)ⁿ⁺¹2ⁿ. Find the sum of the first four terms

Explanation

Step 1: Find T₁ (n = 1)
T₁ = (-1)¹⁺¹ × 2¹
= (-1)² × 2
= 1 × 2 = 2

Step 2: Find T₂ (n = 2)
T₂ = (-1)²⁺¹ × 2²
= (-1)³ × 4
= -1 × 4 = -4

Step 3: Find T₃ (n = 3)
T₃ = (-1)³⁺¹ × 2³
= (-1)⁴ × 8
= 1 × 8 = 8

Step 4: Find T₄ (n = 4)
T₄ = (-1)⁴⁺¹ × 2⁴
= (-1)⁵ × 16
= -1 × 16 = -16

Step 5: Calculate sum
Sum = 2 + (-4) + 8 + (-16)
= 2 – 4 + 8 – 16
= 10 – 20
= -10