The nth term of the sequence -2, 4, -8, 16.... is given by

Analyze the question The sequence is -2, 4, -8, 16, ... and we need the formula for the nth term. The options appear to have lost their superscripts in formatting. Option B almost certainly means Tₙ = (-2)ⁿ, and A means 2ⁿ.

Explain the concept This is a geometric progression (GP), where each term is found by multiplying the previous term by a constant ratio r. The nth term is Tₙ = arⁿ⁻¹.

Solution

• First term: a = -2
• Common ratio: r = 4 ÷ (-2) = -2
• Check: -8 ÷ 4 = -2 ✓ and 16 ÷ (-8) = -2 ✓

Using Tₙ = arⁿ⁻¹:

Tₙ = (-2)(-2)ⁿ⁻¹ = (-2)ⁿ

Verify with the terms:

• n = 1: (-2)¹ = -2 ✓
• n = 2: (-2)² = 4 ✓
• n = 3: (-2)³ = -8 ✓
• n = 4: (-2)⁴ = 16 ✓

Now the other options (read as powers):

• A. 2ⁿ gives 2, 4, 8, 16, which has no alternating signs ✗
• C. -2ⁿ gives -2, -4, -8, ..., which is always negative ✗
• D. nⁿ gives 1, 4, 27, ... ✗

If the options were read literally without powers, B would be (-2)·n = -2n, giving -2, -4, -6, which would not match. So the question clearly intends the exponent form, and B is the one that works.

Answer: B, Tₙ = (-2)ⁿ

Exam tip: When the signs alternate, the common ratio is negative. Test n = 1, 2, 3 in each option. If the first term is a and the ratio r is equal to a, then Tₙ = aⁿ directly.