What is the missing number? 4, -8, 16, (?), 64, -128

Concept

In a geometric sequence each term is obtained by multiplying the previous term by a fixed number called the common ratio (r). To find r, divide any term by the term just before it: r = term / previous term. A constant r confirms the pattern is geometric, and any missing term equals the term before it multiplied by r.

Application

1. List the known terms in order: 4, -8, 16, ?, 64, -128.

2. Find the common ratio from the first pair: (-8) / 4 = -2.

3. Confirm it repeats: 16 / (-8) = -2, so r = -2 holds across the early terms.

4. The missing term sits right after 16, so multiply: 16 x (-2) = -32.

So the value at the (?) position is -32.

Cross-check

Move forward from -32 with the same ratio: (-32) x (-2) = 64, and 64 x (-2) = -128. Both of these match the terms already given, which confirms -32 is consistent with the whole sequence. Note the sign alternates (+, -, +, -, ...) because r is negative, so the missing slot, following a positive 16, must be negative.